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Seminar on

Mathematical General Relativity

Organizers:

 Philippe G. LeFloch (Univ. Pierre et Marie Curie)

Ghani Zeghib (Ecole Normale Supérieure, Lyon)

With the financial support of the ANR Project

“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

Thursday February 9, 2012

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

Lecture room 15-25 101 (first level)

14h   Alan Rendall (AEI, Potsdam) Singularity formation in solutions of the Einstein-Vlasov system

Abstract.  Important questions in mathematical relativity are when singularities form in solutions of the Einstein equations coupled to matter and, in cases where they do form, what their qualitative nature is. A type of matter model which apparently rarely loses smoothness in the absence of black hole formation is collisionless matter modelled by the Vlasov equation. This contrasts with dust, a type of matter popular among relativists. In this talk I describe recent work with Juan Velazquez where we try to obtain new insights about the dynamics of the Einstein-Vlasov system by interpolating between smooth Vlasov and dust in a suitable way. We have shown that for certain mildly singular initial data a curvature singularity can form. It is constructed by means of a shooting argument for a system of ordinary differential equations. From the point of view of physics it would be desirable to improve this solution in various ways and I will report briefly on work in progress on doing this.

15h30 François Filastre (Cergy-Pontoise) Brunn–Minkowski theory in Minkowski spacetime 

Abstract.  The Brunn–Minkowski theory deals with the relations between the addition and the volume of convex bodies of the Euclidean space. Convex bodies are described by function on the sphere. The main result of the theory is that the volume is log-concave. We establish an analog result for a class of convex sets in the Minkowski spacetime. The compactness is replaced by a global invariance property under the action of particular groups of linear isometries. In particular, these convex sets can be described by functions on compact hyperbolic manifolds and, in this case, the volume is convex.

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7th DFG–CNRS WORKSHOP

Two-Phase Fluid Flows. Modeling and Computational Methods 

Main organizer:    

 Philippe G. LeFloch (Univ. Pierre et Marie Curie, Paris)

Co-organizers:

Christophe Berthon (Nantes) and Philippe Helluy (Strasbourg)

With financial support from the DFG and the CNRS

Tuesday Feb. 14, 2012 at 2pm to Thursday Feb. 16 at noon

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, Place Jussieu, Paris.

Subway station: Jussieu

Lecture room 15-16 — 309

TITLES and ABSTRACTS

Gonca Aki (Berlin) An incompressible diffuse flow with phase transition

Mathieu Bachmann (Aachen) Numerical simulation of shock wave-bubble interactions using laser-induced cavitation bubbles

Frank Boyer (Marseille)  Numerical methods for a three-component phase field model

Sergey L. Gavrilyuck (Marseille) Diffuse interface model for compressible fluid-compressible elastic-plastic solid interaction

Maren Hantke (Magdeburg) Exact solutions to the Riemann problem for compressible isothermal Euler equations for two phase flows, with and without phase transition

Philippe Helluy  (Strasbourg) Computing bubble oscillations on GPU (graphics processing unit)

Dietmar Kroener (Freiburg) Numerics for phase field models

Hélène Mathis (Nantes) Model adaptation for hyperbolic systems with relaxation 

Khaled Saleh (Paris) A splitting method for the isentropic Baer-Nunziato two-phase flow model 

Nicolas Seguin (Paris)  Model adaptation in hierarchies of hyperbolic systems

Gabriele Witterstein (Munich) Existence of transition profiles for compressible flows

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PRACTICAL INFORMATIONS

The PROGRAM will be posted here (later)

To be included on the LIST OF PARTICIPANTS, send me an email at:  contact@philippelefloch.org

How to come to the Laboratoire Jacques-Louis Lions ?

Hotels near the University Pierre et Marie Curie ?

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EARLIER WORKSHOPS “Micro-Macro Modeling and Simulation of Liquid-Vapour Flows”

Sixth Workshop, Stuttgart, Jan. 2011

Fourth Workshop, Aachen, Feb. 2009

Second Workshop, Bordeaux

Opening Workshop, Kirchzarten, Nov. 2005

Seminar on Compressible Fluids

Tuesday January 10, 2012

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie

4 Place Jussieu, 75258  Paris

Building 15/16. Lecture room 309

With the support of LRC MANON

• 14h00 : Philippe Helluy (Strasbourg) Résolution des équations de Maxwell-Vlasov sur GPU

Abstract.  Je présenterai un couplage d’une méthode Galerkin-Discontinu et d’une méthode PIC (Particle-In-Cell) pour la résolution des équations de Vlasov-Maxwell. Ces méthodes ont déjà été implémentées à de nombreuses reprises. La nouveauté consiste ici à le faire sur une carte graphique avec le langage OpenCL, ce qui conduit à des façons différentes d’organiser l’algorithme de couplage.

• 15h30 : Christophe Berthon (Nantes)  Schémas hydrostatiques décentrés pour les équations shallow-water

Abstract.  We consider the numerical approximation of the shallow–water equations with non–flat topography. We introduce a new topographic discretization which makes all schemes to be well–balanced and robust. In contrast with the well–known hydrostatic reconstruction, the proposed numerical procedure does not involve any cut–off. Moreover, the proposed scheme is able to deal with dry areas. Several numerical benchmarks are presented to assert the interest of the method.

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Organizers: Frédéric Coquel, Edwige Godlewski, et Philippe LeFloch

Filed under: ALL SEMINARS AND CONFERENCES, COMPRESSIBLE FLUIDS Tagged: Math Fluids ]]> http://philippelefloch.wordpress.com/2011/12/07/seminar-on-compressible-fluids-january-10-2012/feed/ 0 Philippe LeFloch http://philippelefloch.wordpress.com/2011/12/02/seminar-on-mathematical-general-relativity-january-5-2012/ http://philippelefloch.wordpress.com/2011/12/02/seminar-on-mathematical-general-relativity-january-5-2012/#comments Fri, 02 Dec 2011 21:00:36 +0000 Philippe LeFloch http://philippelefloch.wordpress.com/?p=1782 ]]>

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Seminar on

Mathematical General Relativity

Organizers:

 Philippe G. LeFloch (Univ. Pierre et Marie Curie)

Ghani Zeghib (Ecole Normale Supérieure, Lyon)

With the financial support of the ANR Project

“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

Thursday January 5, 2012

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

Lecture room 15-25 326 (third floor)

14h  Alain Bachelot (Bordeaux) Klein-Gordon equation on the Anti-de Sitter universe AdS5

Abstract.  We consider the Klein-Gordon equation on the Poincaré chart of the 5-dimensional Anti-de Sitter universe. When the mass is larger than −1, the Cauchy problem is well posed despite the loss of global hyperbolicity due to the time-like horizon. We express all finite energy solutions in the form of a continuous Kaluza-Klein tower. We investigate the case of gravitational fluctuations, and  electromagnetic waves. The propagation of the wave front set shows that the horizon acts like a perfect mirror. We establish several results on the asymptotic behavior: dispersive estimates, global Strichartz estimates, existence of a lacuna, equi-partition of the energy. We address the cosmological model of the `negative tension’ Minkowski brane. We prove that the hyperbolic mixed problem is well-posed and that all normalizable solutions can be expanded in a discrete Kaluza-Klein tower. Finally, we obtain some L2−L∞ estimates in suitable weighted Sobolev spaces.

15h30 Gilles Carron (Nantes) Rigidity of critical metrics

Abstract. We explain how an elementary idea (existence of bubble of curvature) can be used to proved new and old rigidity results for critical metrics. For instance, we re-prove an old result by M. Anderson that, for an Einstein metric, we get a control on the curvature from a control on the volume.

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Seminar on

Mathematical General Relativity

Organizers:

 Philippe G. LeFloch (Univ. Pierre et Marie Curie)

Ghani Zeghib (Ecole Normale Supérieure, Lyon)

With the financial support of the ANR Project

“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

Thursday Nov. 24, 2011

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

Lecture room 15-25 326 (third floor)

14h   Paul Laurain (Paris 7)  Surfaces with constant mean curvature in a Riemannian manifold of  dimension 3

Abstract.  The surfaces with constant mean curvature (CMC) in a spacelike hypersurface are geometrically and physically very interesting, as shown by Huisken and Yau in 1996 or in the beautiful thesis of Bray. However, the purpose of this talk is not to develop the physical properties of CMC surfaces but to see on an example what are the analytical difficulties encountered when studying these surfaces. In fact, we will  show how to study CMC surfaces in terms of partial differential equations in order to derive geometric properties. We emphasize in particular the key difficulties generated by the conformal invariance of the problem as the phenomena of concentration and we will show how the structure of the equation helps us to overcome them.

15h30  James D.E. Grant (Vienna)  Null injectivity radius estimates

Abstract. I will report on joint work with P.G. LeFloch, in which we use comparison techniques, such as the Rauch comparison theorem and Hessian comparison theorem, to estimate the null injectivity radius on a Lorentzian manifold. This work gives a more geometrical setting for work of Klainerman and Rodnianski on null injectivity radius estimates.

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Seminar on

Mathematical General Relativity

Organizers:

 Philippe G. LeFloch (Univ. Pierre et Marie Curie)

Ghani Zeghib (Ecole Normale Supérieure, Lyon)

With the financial support of the ANR Project

“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

Thursday November 3, 2011

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

Lecture room 15-25 326 (third floor)

14h   Charles Boubel (Strasbourg) Germs of Lorentzian metrics and holonomy

Abstract.  The holonomy group of a pseudo-Riemannian metric g -so e.g. a Riemannian or a Lorentzian metric- is a subgroup of O(g) which indicates, in a certain sense, how much its Levi-Civita connection fails to be flat. A central task related to those groupes is to determine the list of the subgroups of O(g) arising as holonomy, and for each item, to parametrize the set of corresponding metrics and build global examples (i.e. complete or compact). In the Riemannian case, this work is now done. We will see that, regarding holonomy matters, Lorentzian metrics behave totally differenly from Riemannian ones. I will review works of L. Bérard-Bergery, A. Ikemakhen, T. Leistner, A. Galaev, and myself, that together deal with the local aspect of the question.

15h30  David Parlongue (Nice) Breakdown criteria and extendibility in general relativity

Abstract. We will begin this talk by reviewing a geometric breakdown criterion for Einstein’s vacuum equations introduced by S. Klainerman and I. Rodnianski and various improvements (non-vacuum case, integral conditions, various gauge choices). We will then examine a spacetime localization of these criteria. We will focus on consequences in terms of formation of singularities, extendibility of spacetimes, and local regularity of foliations.

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Seminar on

Mathematical General Relativity

Organizers:

 Philippe G. LeFloch (Univ. Pierre et Marie Curie)

Ghani Zeghib (Ecole Normale Supérieure, Lyon)

With the financial support of the ANR Project

“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

Thursday September 29, 2011

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

Lecture room 15-25 1-01 (first floor)

14h  Robert Beig (Vienna) Elastic perturbations of static perfect fluid bodies: Newtonian theory 

Abstract.  We describe a model for static self-gravitating bodies with both fluid and elastic properties. This should allow for a rigorous existence theory of solutions near a perfect fluid configuration, e.g. ‘putting mountains on a neutron star’.

15h30 Jacques Smulevici (Orsay) Wave equations on asymptotically AdS black hole 

Abstract. This is joint work with Gustav Holzelgel.  We prove a logarithmic decay estimate for solutions of the linear wave equation on a slowly rotating Kerr-Anti-de-Sitter spacetime. This estimate is expected to be sharp in view of heuristics and numerics from the physics litterature. The underlying reason for the slow decay rate established here can be traced back to a stable trapping phenomenon for asymptotically anti de Sitter black holes near infinity.

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Seminar on

Mathematical General Relativity

Organizers: Sergiu Klainerman (Princeton)

Philippe G. LeFloch (Univ. Pierre et Marie Curie) Gabriele Veneziano (Collège de France)

With the financial support of  the Fondation des Sciences Mathématiques de Paris

Monday June 13, 2011

Institut Henri Poincaré, Paris, Lecture room 314

11h  Lars Andersson (Potsdam) Linear fields on Kerr spacetime   

Abstract. The problem of nonlinear stability for the Kerr model of a rotating black hole is one of the central problems in general relativity.  The analysis of linear fields of spin 0, 1, 2, on the Kerr spacetime is an important model problem for full nonlinear stability. I will report on recent progress on this problem.

14h  Yvonne Choquet-Bruhat (IHES, Bures-sur-Yvette)  Positive gravitational energy in arbitrary dimensions

Abstract. The most elegant and convincing proof of the positive energy theorem is by using spinors, as did Witten in the dimension 3 +1, inspired by heuristic works of Deser and Grisaru originating from supergravity. Our aim here  is to present a streamlined, complete proof, valid in arbitrary space dimensions, and using only spinors on an oriented Riemannian space, without invoking spacetime spinors.

Seminar on Compressible Fluids

Wednesday May 18, 2011

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie

4 Place Jussieu, 75258  PARIS

Jussieu campus. Building 15/16. Lecture room 309.

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• 11h – Siddhartha MISHRA (ETH, Zurich) Entropy stable high-order schemes for systems of conservation laws

Abstract. We design arbitrarily high-order schemes for systems of conservation laws that satisfy a discrete version of the entropy inequality. Consequently, these schemes are stable in L2. The proposed schemes are based on a combination of arbitrarily high-order entropy conservative schemes together with numerical diffusion operators. The numerical diffusion operators require an ENO reconstruction of the entropy variables. The resulting schemes are shown to be entropy stable for conservation laws in several space dimensions. Recent work extending these schemes to the fully discrete case and to unstructured meshes based on a shock-capturing space time Discontinuous Galerkin (DG) method will be mentioned. Numerical experiments illustrating the robust performance of the proposed schemes are presented. The talk is based on joint work with U. S. Fjordholm, A. Hiltebrand (ETH, Zurich) and E. Tadmor (University of Maryland, U.S.A).

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Organizers. Frédéric Coquel, Edwige Godlewski, Philippe LeFloch

Seminar on Compressible Fluids

Wednesday March 30, 2011

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie

4 Place Jussieu, 75258  PARIS

Jussieu campus. Building 15/16. Lecture room 309.

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• 10h00 : François Gay-Balmaz (ENS, Paris) Intégrateurs variationels pour les fluides géophysiques

Abstract. Récemment, des nouvelles méthodes numériques ont été formulées pour résoudre les équations d’Euler incompressible. Il s’agit d’intégrateurs variationels basés sur la discrétisation du groupe des difféomorphismes qui préservent le volume. Ces nouvelles méthodes ont des propriétés attrayantes : - elles conservent l’énergie et les théorèmes de circulation de Kelvin, – elles ne sont pas plus coûteuses que des méthodes de différences finies ordinaires, – elles respectent la structure géométrique et Hamiltonienne des équations, – elles sont applicables sur des grilles 2D ou 3D non structurées. Dans ce séminaire nous présentons ces nouvelles méthodes et montrons comment les généraliser aux modèles de fluides géophysiques (Boussinesq, équations primitives) tout en respectant les bonnes propriétés énoncées ci-dessus.

• 11h15 : Corrado Mascia (Rome) Two phase solutions for a forward-backward equation

Abstract. We consider a nonlinear diffusion equation with a cubic-like diffusion function arising in the context of phase transitions (in the spirit of the Cahn–Hilliard equation). Because of the non-monotonicity of the diffusion function, the Cauchy problem is ill-posed. To restore the well-posedness, it is possible to take into consideration a generalized formulation determined by considering the forward-backward equation as the singular limit of a corresponding higher order equation, given by the addition of a third order term (two space and one time derivative) of Sobolev type, different with respect to the fourth-space derivative term considered in the case of Cahn–Hilliard equations. Because of some analogies with the case of hyperbolic conservation laws, such kind of solutions has been called entropy solutions for the forward-backward diffusion equation. The aim of the talk is to present and discuss the entropy framework for this equation, with particular attention given to solutions taking values in the zones where the diffusion function is monotone increasing. Joint works with A.Terracina, A. Tesei and P.Lafitte.

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Organizers: Frédéric Coquel, Edwige Godlewski, et Philippe LeFloch

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Seminar on

Mathematical General Relativity

Organizers: Sergiu Klainerman (Princeton)

Philippe G. LeFloch (Univ. Pierre et Marie Curie) Gabriele Veneziano (Collège de France)

With the financial support of  the Fondation des Sciences Mathématiques de Paris

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Monday March 28, 2011

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie

Lecture rooms: 15/25 101  (morning) and 15-/25 102 (afternoon)

11h  Rafe MAZZEO (Stanford) The constraint equation and cylindrical ends

Abstract. This talk will give a closer look at some of the results discussed in last month’s seminar by Piotr Chrusciel concerning our joint work on the existence and classification of solutions of the constraint equations on manifolds with cylindrical ends. I will also describe some new work, with Akutagawa and Carron, concerning the Yamabe equation on stratified spaces, and some regularity theorems for all of these problems.

14h  Jared SPECK (Princeton and MIT) The global stability of the Minkowski spacetime solutions to the Einstein-nonlinear electromagnetic system in wave coordinates

Abstract. The Einstein-nonlinear electromagnetic system is a coupling of the Einstein field equations of general relativity to nonlinear electromagnetic field equations. In this talk, I will discuss the family of covariant electromagnetic models that satisfy the following criteria: i) they are derivable from a sufficiently regular Lagrangian, ii) they reduce to the familiar Maxwell model in the weak-field limit, and iii) their corresponding energy-momentum tensors satisfy the dominant energy condition. I will mention several specific electromagnetic models that are of interest to researchers working in the foundations of physics and in string theory. I will then discuss my main result, which is a proof of the global nonlinear stability of the 1 + 3 dimensional Minkowski spacetime solution to the coupled system. This stability result is a consequence of a small-data global existence result for a reduced system of equations that is equivalent to the original system in a wave coordinate gauge. The analysis of the spacetime metric components is based on a framework recently developed by Lindblad and Rodnianski, which allows one to derive suitable estimates for tensorial systems of quasilinear wave equations with nonlinearities that satisfy the weak null condition. The analysis of the electromagnetic fields, which satisfy quasilinear first-order equations, is based on an extension of a geometric energy-method framework developed by Christodoulou, together with a collection of pointwise decay estimates for the Faraday tensor that I develop. Throughout the analysis, I work directly with the electromagnetic fields, thus avoiding the introduction of electromagnetic potentials.

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Seminar on

Mathematical General Relativity

Organizers: Sergiu Klainerman (Princeton)

Philippe G. LeFloch (Univ. Pierre et Marie Curie) Gabriele Veneziano (Collège de France)

With the financial support of  the Fondation des Sciences Mathématiques de Paris

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Monday March 21, 2011

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie

Lecture rooms: 15/25  1-03 (morning) and 1-02 (afternoon)

11h   Ghani Zeghib (Ecole Normale Supérieure, Lyon) Sur les métriques riemanniennes dégénérées

Abstract. Une métrique riemannienne dégénérée sur une variété est un tenseur qui est une forme quadratique positive (non nécessairement définie) sur l’espace tangent de tout point de la variété. Le noyau de cette forme est un champ de plans(discontinue, e.g. de dimension variable). Le cas riemannien correspond au cas où ce champ est trivial. Le cas le plus proche est celui où ce noya est partout de dimension 1. On appellera une telle structure métrique de lumière. En fait, une métrique sous- riemannienne (de type contact) sur est essentiellement une métrique de lumière sur le fibré cotangent. On se pose ici des questions autour de la rigidité locale d’une telle structure, e.g. du fait qu’elle soit une G-structure de type fini au sens de Cartan.

14h   Willie Wong (Cambridge University, UK) A local characterization of Kerr-Newman spacetimes and some applications

Abstract. In 2000, M. Mars gave a local tensorial characterisation of Kerr space-times based on earlier work of W. Simon. This characterisation was recently used by A. Ionescu and S. Klainerman in their program to study black hole uniqueness (in the vacuum case) without the assumption that the space-time is real analytic. In this talk I will describe a generalisation of the characterisation that applies to electro-vacuum space-times, and survey some results making use of it. Parts of this work is based on joint work with Pin Yu.

Seminar on Compressible Fluids

Wednesday March 16, 2011

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie

4 Place Jussieu, 75258  PARIS

Jussieu campus. Building 15/16. Lecture room 309.

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• 10h00 : Shuichi Kawashima (Kyushu University) Recent progress on the stability analysis for symmetric hyperbolic systems

Abstract. We will discuss the decay property for a class of symmetric hyperbolic systems with relaxation. The Shizuta-Kawashima stability condition gives the characterization of the standard decay structure for systems with symmetric relaxation matrices. Recently, we found several interesting systems with non-symmetric relaxation which have different decay structure. In this talk, we discuss these examples and report the recent progress on the stability theory for a class of symmetric hyperbolic systems.

• 11h30 : Philippe LeFloch (Univ. Pierre et Marie Curie and CNRS) Late-time asymptotic-preserving approximations of hyperbolic equations with stiff relaxation

Abstract. We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff source term. On one hand, we determine the relevant asymptotic expansion, derive a reduced system in the limit, and discuss the role of an entropy condition to establish the diffusive nature of the reduced system. On the other hand, we propose a new numerical scheme of finite volume type, which allows us to recover the correct asymptotic regime. The associated discrete form of the diffusion system is achieved via a suitable discretization compatible with the stiff source term. Our theoretical results are illustrated with several models from continuum physics and numerical experiments demonstrating the relevance of the proposed theory and numerical strategy. (This is a joint work with C. Berthon and R. Turpault.)

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Organizers: Frédéric Coquel, Edwige Godlewski, et Philippe LeFloch

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Seminar on

Mathematical General Relativity

Organizers: Sergiu Klainerman (Princeton)

Philippe G. LeFloch (Univ. Pierre et Marie Curie) Gabriele Veneziano (Collège de France)

With the financial support of  the Fondation des Sciences Mathématiques de Paris

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Monday March 7, 2011

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie

Lecture rooms: 15/25  1-03 (morning) and 1-02 (afternoon)

11h   Jacques Smulevici (AEI, Potsdam)  Weakly regular T2 symmetric spacetimes

Abstract. Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum Einstein spacetimes with T2–symmetry, establish the global well-posedness of the initial value problem for Einstein’s field equations, and investigate the global causal structure of the constructed spacetimes. Our weak regularity assumptions are the minimal ones allowing to give a meaning to the Einstein equations under the assumed symmetry and to solve the initial value problem. First of all, we introduce a frame adapted to the symmetry in which each Christoffel symbol can be checked to belong to Lp for some p. We identify certain cancellation properties taking place in the expression of the Riemann and Ricci curvatures, and this leads us to a reformulation of the initial value problem for the Einstein field equations when the initial data set has weak regularity. Second, we investigate the future development of a weakly regular initial data set. We check that the area R of the orbits of symmetry must grow to infinity in the future timelike directions, and we establish the existence of a global foliation by the level sets of the function R. Our weak regularity assumptions only require that R is Lipschitz continuous while the metric coefficients describing the initial geometry of the orbits of symmetry are in the Sobolev space H1 and the remaining coefficients have even weaker regularity. We develop here the compactness arguments required to cover the natural level of regularity associated with the energy of the system of partial differential equations determined from Einstein’s field equations. This is a joint work in collaboration with P.G. LeFloch (Paris).

14h   Erwann Delay (Univ. Avignon) Recollement des TT tenseurs

Abstract. La méthode de Corvino-Schoen permet de recoller localement et de façon lisse deux solutions des équations de contraintes. Nous verrons que l’on peut d’une façon générale recoller deux éléments du noyau de certains opérateurs à symbole surjectif et non injectif. Par exemple on peut recoller deux champs de vecteurs à divergence nulle ou deux TT-tenseurs. On en déduit par exemple que sur toute boule riemannienne ouverte, l’ensemble des TT-tenseurs lisses à support compact est de dimension infinie. On simplifie ainsi la construction de données initiales CMC.

Seminar on Compressible Fluids

Wednesday February 16, 2011

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie

4 Place Jussieu, 75258  PARIS

Jussieu campus. Building 15/16. Lecture room 309.

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• 10h00 : Benjamin Boutin (Rennes) Coupling techniques for nonlinear hyperbolic equations

Abstract. We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems, based on an augmented formulation which allows for the modeling of the dynamics of interfaces between fluid flows. The main technical difficulty to be overcome lies in the possible resonance effect when wave speeds coincide and global hyperbolicity is lost. As a consequence, non-uniqueness of weak solutions is observed for the initial value problem which need to be supplemented with further admissibility conditions.

• 11h30 : Christophe Berthon (Nantes) Quelques résultats sur la stabilité des solveurs approchés de Riemann pour les équations d’Euler gaz réels

Abstract. Dans cet exposé, on s’intéressera à l’obtention d’inégalités discrètes d’entropie qui doivent être satisfaites par les schémas numériques lors de l’approximation des solutions faibles des équations d’Euler pour une thermodynamique de type gaz réels. Après avoir rappelé quelques résultats, avec une attention toute particulière sur les inégalités discrètes d’entropie pour les schémas de relaxation, nous établissons plusieurs critères de stabilité qui généralisent les résultats précédents. Les résultats proposés présentent un second intérêt puisqu’ils portent uniquement sur le solveur approché de Riemann et aucune étape de « relaxation » (ou de prise en compte d’un terme source raide) n’est ici suggérée.

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Organizers: Frédéric Coquel, Edwige Godlewski, et Philippe LeFloch

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Seminar on

Mathematical General Relativity

Organizers: Sergiu Klainerman (Princeton)

Philippe G. LeFloch (Univ. Pierre et Marie Curie) Gabriele Veneziano (Collège de France)

With the financial support of  the Fondation des Sciences Mathématiques de Paris

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Monday February 14, 2011

Institut Henri Poincaré

Lecture room 01

 

11h – Qian Wang (IHES & Albert Einstein Institute, Potsdam) Breakdown criterion for Einstein Vacuum equations in CMC gauge

Abstract. I will report my recent work on the geometric criterion for the breakdown of Einstein vacuum space-times with the constant mean curvature (CMC) foliation. In this work, the criterion is formulated in terms of time-integrability of the sup- norms of the second fundamental form and derivatives of the lapse function associated to CMC foliation of the space-time. This result is obtained through deriving uniform lower bound on the null radius of injectivity of the light cones. I will sketch the main idea of the proof.

14h – Piotr Chrusciel (Vienna) On the general relativistic constraint equations

Abstract. I will present some new results with Rafe Mazzeo on the construction of solutions of the constraint equations with cylindrical ends.

 

 

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Seminar on

Mathematical General Relativity

Organizers: Sergiu Klainerman (Princeton)

Philippe G. LeFloch (Univ. Pierre et Marie Curie) Gabriele Veneziano (Collège de France)

With the financial support of  the Fondation des Sciences Mathématiques de Paris

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Monday January 31rst, 2011

Institut Henri Poincaré

Lecture room 314

 

11h   Lydia Bieri (Ann Arbor), Geometry of Spacetimes Solving the Einstein-Maxwell Equations in General Relativity and Gravitational Radiation

Abstract. A major goal of mathematical General Relativity (GR) and astrophysics is to precisely describe and finally observe gravitational radiation, one of the predictions of GR. In order to do so, one has to study the null asymptotical limits of the spacetimes for typical sources. Among the latter we find binary neutron stars and binary black hole mergers. In these processes typically mass and momenta are radiated away in form of gravitational waves. D. Christodoulou showed that every gravitational-wave burst has a nonlinear memory. In this talk, we discuss the null asymptotics for spacetimes solving the Einstein-Maxwell (EM) equations, compute the radiated energy and derive limits at null infinity and compare them with the Einstein vacuum (EV) case. The physical insights are based on geometric-analytic investigations of the solution spacetimes.

14h   Jérémie Szeftel (ENS, Paris) Around the bounded L2 curvature conjecture in general relativity

Abstract. We report on recent progress obtained on the construction and control of a parametrix to the homogeneous wave equation on a curved background, where the metric is a rough solution to the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes L2 bounds on the curvature tensor of the metric is a major step towards the proof of the bounded L2 curvature conjecture. This is a joint work with Sergiu Klainerman and Igor Rodnianski.

 

 

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Seminar on

Mathematical General Relativity

Organizers: Sergiu Klainerman (Princeton)

Philippe G. LeFloch (Univ. Pierre et Marie Curie) Gabriele Veneziano (Collège de France)

With the financial support of  the Fondation des Sciences Mathématiques de Paris

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie 4 Place Jussieu, 75258 Paris

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Wednesday January 12, 2011

Building 15/16. Lecture room 309

 

14h00   Pieter Blue (Edinburgh) Decay for the Maxwell field outside a Kerr black hole

15h30   Thierry Barbot (Avignon) Particules dans les espaces-temps à courbure constante

 

 

 

Seminar on Compressible Fluids

Monday January 10, 2011

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie

4 Place Jussieu, 75258  PARIS

Jussieu campus. Building 15/16. Lecture room 309.

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• 10h30 : Nikolaos Sfakianakis (Vienna) Numerical schemes for Hyperbolic conservation laws over non-uniform adaptively redistributed meshes

• 11h45 : Magali Mercier (Orléans) Stabilité L1 des lois de conservation scalaires. Applications  au trafic piéton et aux interactions groupe/agent isolé

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Organizers: Frédéric Coquel, Edwige Godlewski, et Philippe LeFloch

Seminar on Compressible Fluids

Monday December 13, 2010

Laboratoire Jacques-Louis Lions

Université Pierre et Marie Curie

4 Place Jussieu, 75258  PARIS

Jussieu campus. Building 15/16. Lecture room 309.

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• 10h30 : Boris Andreanov (Besançon) Dissipative boundary conditions for scalar conservation laws

• 11h30 : Rodolphe Turpault (Nantes)   Late-time relaxation limits of nonlinear hyperbolic systems

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Organizers: Frédéric Coquel, Edwige Godlewski, et Philippe LeFloch