GEOWAKI
Financiado
The analysis of geometric non linear wave and kinetic equations
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 eq...
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.
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Duración del proyecto: 68 meses
Fecha Inicio: 2016-11-08
Fecha Fin: 2022-07-31
Fecha Fin: 2022-07-31
Línea de financiación: concedida
El organismo H2020 notifico la concesión del proyecto el día 2022-07-31
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2016-STG:
ERC Starting Grant
Cerrada
hace 9 años
Presupuesto
El presupuesto total del proyecto asciende a
1M€
Líder del proyecto
SORBONNE UNIVERSITE
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5
475.69K€ |
Participante