Optimal Regularizing Effect for Scalar Conservation Laws

François Golse (1, 2) , Benoît Perthame (1, 3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 CMLS - Centre de Mathématiques Laurent Schwartz
3 BANG - Nonlinear Analysis for Biology and Geophysical flows

We investigate the regularity of bounded weak solutions of scalar conservation laws with convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure. The proof is based on the kinetic formulation of scalar conservation laws and on an interaction estimate in physical space.

Mots clés: Scalar conservation law; Compensated compactness; Regularizing effect; Kinetic formulation

Domaines: Equations aux dérivées partielles [math.AP]

François Golse, Benoît Perthame. Optimal Regularizing Effect for Scalar Conservation Laws. Revista Matemática Iberoamericana, 2013, 29 (2013), pp.1477-1504. ⟨10.4171/rmi/765⟩. ⟨hal-00650350v2⟩