- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:47
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
29
2013
4
Optimal regularizing effect for scalar conservation laws
François
Golse
École Polytechnique, PARIS, FRANCE
Benoît
Perthame
Université Pierre et Marie Curie, PARIS CEDEX 05, FRANCE
Scalar conservation law, compensated compactness, regularizing effect, kinetic formulation
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
Partial differential equations
Fluid mechanics
1477
1504
10.4171/RMI/765
http://www.ems-ph.org/doi/10.4171/RMI/765