On the global evolution of self-gravitating matter. Nonlinear interactions in Gowdy symmetry - Laboratoire Jacques-Louis Lions Accéder directement au contenu
Article Dans Une Revue Arch.Ration.Mech.Anal. Année : 2019

On the global evolution of self-gravitating matter. Nonlinear interactions in Gowdy symmetry

Bruno Le Floch

Résumé

We are interested in the evolution of a compressible fluid under its self-generated gravitational field. Assuming here Gowdy symmetry, we investigate the algebraic structure of the Euler equations satisfied by the mass density and velocity field. We exhibit several interaction functionals that provide us with a uniform control on weak solutions in suitable Sobolev norms or in bounded variation. These functionals allow us to study the local regularity and nonlinear stability properties of weakly regular fluid flows governed by the Euler-Gowdy system. In particular for the Gowdy equations, we prove that a spurious matter field arises under weak convergence, and we establish the nonlinear stability of weak solutions.

Dates et versions

hal-01815151 , version 1 (13-06-2018)

Identifiants

Citer

Bruno Le Floch, Philippe G. Lefloch. On the global evolution of self-gravitating matter. Nonlinear interactions in Gowdy symmetry. Arch.Ration.Mech.Anal., 2019, 233 (1), pp.45-86. ⟨10.1007/s00205-018-01354-5⟩. ⟨hal-01815151⟩
90 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More