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arXiv · 1808.00289

Non existence of the BV regularizing effect for scalar conservation laws in several space dimension

Shyam Sundar Ghoshal·Animesh Jana
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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.

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Shyam Sundar Ghoshal, Animesh Jana. 2018-08-01. Non existence of the BV regularizing effect for scalar conservation laws in several space dimension. https://arxiv.org/abs/1808.00289

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