Non existence of the BV regularizing effect for scalar conservation laws in several space dimension
Analysis of PDEs
2020-10-08 v3
Abstract
This article deals with the regularity aspects of entropy solutions to scalar conservation laws. We show that for each C2 flux in multi-D, there exists an entropy solution which does not belong to BV locally for all time. For this purpose, we construct a non-BVloc solution in 1-D for a special class of C2 fluxes whose second derivative has a zero. It covers all the C2 functions for which Lax-Oleinik's BV regularizing result is not applicable and provides a classification of one dimensional C2 fluxes based on L\infty-BVloc regularizing of entropy solution. In the later part of this article, we extend our result to fractional Sobolev spaces for a class of non-degenerate fluxes.
Keywords
Cite
@article{arxiv.1808.00289,
title = {Non existence of the BV regularizing effect for scalar conservation laws in several space dimension},
author = {Shyam Sundar Ghoshal and Animesh Jana},
journal= {arXiv preprint arXiv:1808.00289},
year = {2020}
}