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The analysis of geometric non-linear wave and kinetic equations

Total Cost €


EC-Contrib. €






Project "GEOWAKI" data sheet

The following table provides information about the project.


Organization address
city: PARIS
postcode: 75006
website: n.a.

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Total cost 1˙071˙008 €
 EC max contribution 1˙071˙008 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2017
 Duration (year-month-day) from 2017-02-01   to  2022-01-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    SORBONNE UNIVERSITE FR (PARIS) coordinator 841˙008.00
2    UNIVERSITE PARIS-SACLAY FR (SAINT AUBIN) participant 230˙000.00


 Project objective

The present proposal is concerned with the analysis of geometric non-linear wave equations, such as the Einstein equations, as well as coupled systems of wave and kinetic equations such as the Vlasov-Maxwell and Einstein-Vlasov equations. We intend to pursue three main lines of research, each of them concerning major open problems in the field. I) The dynamics in a neighbourhood of the Anti-de-Sitter space with various boundary conditions. This is a fundamental open problem of mathematical physics which aims at understanding the stability or instability properties of one of the simplest solutions to the Einstein equations. On top of its intrinsic mathematical interest, this question is also at the heart of an intense research activity in the theoretical physics community. II) Non-linear systems of wave and kinetic equations. We have recently found out that the so-called vector field method of Klainerman, a fundamental tool in the study of quasilinear wave equations, in fact possesses a complete analogue in the case of kinetic transport equations. This opens the way to many new directions of research, with applications to several fundamental systems of kinetic theory, such as the Einstein-Vlasov or Vlasov-Maxwell systems, and creates a link between two areas of PDEs which have typically been studied via different methods. One of our objectives is to develop other potential links, such as a general analysis of null forms for relativistic kinetic equations. III) The Einstein equations with data on a compact manifold. The long time dynamics of solutions to the Einstein equations arising from initial data given on a compact manifold is still very poorly understood. In particular, there is still no known stable asymptotic regime for the Einstein equations with data given on a simple manifold such as the torus. We intend to establish the existence of such a stable asymptotic regime.


year authors and title journal last update
List of publications.
2020 Fournodavlos, Grigorios; Smulevici, Jacques
On the initial boundary value problem for the Einstein vacuum equations in the maximal gauge
published pages: , ISSN: , DOI: 1 2020-04-15
2020 Jabiri, Fatima Ezzahra
Static spherically symmetric Einstein-Vlasov bifurcations of the Schwarzschild spacetime
published pages: , ISSN: , DOI: 1 2020-04-15
2019 Bigorgne , Léo
Sharp asymptotic behavior of solutions of the $3d$ Vlasov-Maxwell system with small data
published pages: , ISSN: , DOI: 1 2020-03-11
2019 Léo Bigorgne
A vector field method for massless relativistic transport equations and applications
published pages: , ISSN: , DOI:
arxiv 2020-03-11
2019 Xianglong Duan
Sharp Decay Estimates for the Vlasov-Poisson and Vlasov-Yukawa Systems with Small Data
published pages: , ISSN: , DOI:
arxiv 2020-03-11
2017 Léo Bigorgne
Asymptotic properties of small data solutions of the Vlasov-Maxwell system in high dimensions
published pages: , ISSN: , DOI:
2019 Grigorios Fournodavlos, Volker Schlue
On “Hard Stars” in General Relativity
published pages: 2135-2172, ISSN: 1424-0637, DOI: 10.1007/s00023-019-00793-4
Annales Henri Poincaré 20/7 2020-03-11
2018 Fajman, David; Joudioux, Jérémie; Smulevici, Jacques
The Stability of the Minkowski space for the Einstein-Vlasov system
published pages: , ISSN: , DOI: 3 2020-03-11
2019 Bigorgne, Léo
Sharp asymptotics for the solutions of the three-dimensional massless Vlasov-Maxwell system with small data
published pages: , ISSN: , DOI: 2 2020-03-11
2017 Fajman, David; Joudioux, Jérémie; Smulevici, Jacques
\"Sharp asymptotics for small data solutions of the Vlasov-Nordstr\"\"om system in three dimensions\"\"\"
published pages: , ISSN: , DOI:
2 2020-03-11
2019 Bigorgne , Léo
Asymptotic properties of the solutions to the Vlasov-Maxwell system in the exterior of a light cone
published pages: , ISSN: , DOI: 2020-03-11
2017 Jacques Smulevici, David Fajman, Jérémie Joudioux
Vector field methods for kinetic equations with applications to classical and relativistic systems
published pages: , ISSN: , DOI:
Séminaire Laurent Schwartz—Équations aux dérivées partielles et applications Année 2016–2017, Exp. No. II 2020-03-11

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