Nonlinear regularizing effect for hyperbolic partial differential equations

François Golse (1, 2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LJLL - Laboratoire Jacques-Louis Lions

The Tartar-DiPerna compensated compactness method, used initially to construct global weak solutions of hyperbolic systems of conservation laws for large data, can be adapted in order to provide some regularity estimates on these solutions. This note treats two examples: (a) the case of scalar conservation laws with convex flux, and (b) the Euler system for a polytropic, compressible fluid, in space dimension one.

Mots clés: Hyperbolic systems; Compensated compactness; Regularizing effect; Scalar conservation law; Isentropic Euler system

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

François Golse. Nonlinear regularizing effect for hyperbolic partial differential equations. XVIth International Congress on Mathematical Physics, Aug 2009, Prague, Czech Republic. pp.433-437. ⟨hal-00472351⟩