Revista Matemática Iberoamericana

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Volume 29, Issue 4, 2013, pp. 1477–1504
DOI: 10.4171/RMI/765

Published online: 2013-12-15

Optimal regularizing effect for scalar conservation laws

François Golse[1] and Benoît Perthame[2]

(1) École Polytechnique, Paris, France
(2) Université Pierre et Marie Curie, Paris, France

We investigate the regularity of bounded weak solutions of scalar conservation laws with uniformly convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure. We prove that all such solutions belong to the Besov space $B^{1/3,3}_{\infty,{\rm loc}}$. Since C. de Lellis and M. Westdickenberg [11] have proved the existence of such solutions that do not belong to $B^{s,p}_{q,{\rm loc}}$ if either $s>1/\max(p,3)$ or $s=1/3$ and $1\le q

Keywords: Scalar conservation law, compensated compactness, regularizing effect, kinetic formulation

Golse François, Perthame Benoît: Optimal regularizing effect for scalar conservation laws. Rev. Mat. Iberoamericana 29 (2013), 1477-1504. doi: 10.4171/RMI/765