Optimal regularity for all time for entropy solutions of conservation laws in $$BV^s

This paper deals with the optimal regularity for entropy solutions of conservation laws. For this purpose, we use two key ingredients: (a) fine structure of entropy solutions and (b) fractional BV spaces. We show that optimality of the regularizing effect for the initial value problem from $L^\infty...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear differential equations and applications 2020-10, Vol.27 (5), Article 46
Main Authors: Ghoshal, Shyam Sundar, Guelmame, Billel, Jana, Animesh, Junca, Stéphane
Format: Article
Language:English
Subjects:
Analysis of PDEs
Mathematics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper deals with the optimal regularity for entropy solutions of conservation laws. For this purpose, we use two key ingredients: (a) fine structure of entropy solutions and (b) fractional BV spaces. We show that optimality of the regularizing effect for the initial value problem from $L^\infty$ to fractional Sobolev space and fractional BV spaces is valid for all time. Previously, such optimality was proven only for a finite time, before the nonlinear interaction of waves. Here for some well-chosen examples, the sharp regularity is obtained after the interaction of waves. Moreover , we prove sharp smoothing in $BV^s$ for a convex scalar conservation law with a linear source term. Next, we provide an upper bound of the maximal smoothing effect for nonlinear scalar multi-dimensional conservation laws and some hyperbolic systems in one or multi-dimension.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-020-00649-5