Mathematical General Relativity, Compressible Fluids, and More

J. Hyperbolic Differential Equations (JHDE)

In GENERAL RELATIVITY, J. Hyperbolic Differential Equations (JHDE) on September 7, 2009 at 11:20 am


Main Editor: Philippe G. LeFloch

Laboratoire Jacques-Louis Lions
Centre National de la Recherche Scientifique (CNRS)
Université Pierre et Marie Curie
(Paris 6), 4 Place Jussieu
75252 Paris, FRANCE

Co-editor:  Jian-Guo Liu, Duke Univ.

Editorial Board

  • Lars Andersson (Potsdam)
  • François Bouchut (Paris-Est)
  • Shuxing Chen (Shanghai)
  • James Colliander (Toronto)
  • Rinaldo M Colombo (Brescia)
  • Constantine M Dafermos (Providence)
  • Helmut Friedrich (Potsdam)
  • Kenneth H Karlsen (Oslo)
  • Shuichi Kawashima (Fukuoka)
  • Sergiu Klainerman (Princeton)
  • Peter D Lax (New York)
  • Tai-Ping Liu (Taipei)
  • Pierro Marcati (L’Aquila)
  • Nader Masmoudi (New York)
  • Frank Merle (Bures-sur-Yvette)
  • Cathleen S Morawetz (New York)
  • Tatsuo Nishitani (Osaka)
  • Alan D Rendall (Potsdam)
  • Denis Serre (Lyon)
  • Eitan Tadmor (College Park)

This journal publishes original research papers on nonlinear hyperbolic problems and related topics, especially on the theory and numerical analysis of hyperbolic conservation laws and on hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in:

  • Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions.
  • Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models.
  • Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations.
  • Nonlinear hyperbolic systems arising in continuum physics such as hyperbolic models of fluid dynamics, mixed models of transonic flows.
  • General problems that are dominated by finite speed phenomena such as dissipative and dispersive perturbations of hyperbolic systems, and models relevant to the derivation of fluid dynamical equations.

JHDE aims to provide a forum for the community of researchers working in the very active area of nonlinear hyperbolic problems and nonlinear wave equations, and will also serve as a source of information for the applications.



Three-Month Program on MATHEMATICAL GENERAL RELATIVITY at the Institut Henri Poincaré



Lars Andersson (Potsdam)

Sergiu Klainerman (Princeton) 

Philippe G. LeFloch (Paris) 



September 14, 2015 to December 18, 2015


Main Themes of the Program

Einstein’s field equation of general relativity is one of the most important geometric partial differential equations. Over the past decade, the mathematical research on Einstein equation has made spectacular progress on many fronts (Cauchy problem, cosmic censorship, asymptotic behavior). These developments have brought into focus the deep connections between the Einstein equation and other important geometric PDE’s, including the wave map equation, Yang-Mills equation, Yamabe problem, as well as Hamilton’s Ricci flow. The field is of growing interest for mathematicians and of intense current activity, as is illustrated by major recent breakthrough, concerning the uniqueness and stability of the Kerr black hole model, the formation of trapped surfaces, and the bounded L2 curvature problem. Specifically, the themes of mathematical interest that will be developed in the present Program and are currently most active include:

  •  The initial value problem for Einstein equation and the causal geometry of spacetimes with low regularity, formation of trapped surfaces
  • Techniques of Lorentzian geometry: injectivity radius estimates, geometry of null cones; construction of parametrices
  •  Geometry of black hole spacetimes: uniqueness theorems, censorship principles
  • Coupling of Einstein equation for self-gravitating matter models, weakly regular spacetimes with symmetry

Main Events

  • Week of Sept. 18, 2015: Summer School
  • Week of Sept. 25, 2015: Conference on mathematical properties of spacetimes and black holes
  • Oct. 2015: Conference on self-gravitating matter models
  • Week of Nov. 16, 2015: Conference on mathematical methods in general relativity

Program coordinated by the Centre Emile Borel at IHP. Financial support provided by the Institut Henri Poincaré and the ANR Project “Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”.

Seminar on Mathematical General Relativity – Wednesday February 12, 2014


Seminar on

Mathematical General Relativity


 Philippe G. LeFloch (Paris)

Jérémie Szeftel (Paris) 

Ghani Zeghib (Lyon)


ANR Project

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

February 12, 2014

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

Lecture room  1525-103

14h  Florian Beyer  (Dunedin)  Graceful exit from inflation for minimally coupled Bianchi A scalar field models

Abstract. We consider the dynamics of Bianchi A scalar field models which undergo inflation. The main question is under which conditions does inflation come to an end and is succeeded by a decelerated epoch. This so-called ‘graceful exit’ from inflation is an important ingredient in the standard model of cosmology, but is, at this stage, only understood for restricted classes of solutions. We present new results obtained by a combination of analytical and numerical techniques.

15h30  Cécile Huneau (ENS, Paris)  Vacuum constraint equations for asymptotically flat space-times with a translational Killing field

Abstract. In the presence of a space-like translational Killing field, vacuum Einstein equations in 3+1 dimensions reduces to 2+1 Einstein equations with a scalar field. Minkowski space-time is a trivial solution of vacuum Einstein equation with a translational Killing field. A natural question is therefore the nonlinear stability of Minkowski solution in this setting. A first step in addressing this problem is the study of the constraint equations. The main difficulty in that case is due to the delicate inversion of the Laplacian. In particular, we have to work in the non constant mean curvature setting, which enforces us to consider the intricate coupling of the Einstein constraint equations.


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