Higher Regularity for Entropy Solutions of Conservation Laws with Geometrically Constrained Discontinuous Flux

For the Burgers equation, the entropy solution becomes instantly BV with only $ L^\infty$ initial data. For conservation laws with genuinely nonlinear discontinuous flux, it is well known that the BV regularity of entropy solutions is lost. Recently, this regularity has been proved to be fractional...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 2024-01, Vol.56 (5), p.6121-6136
Main Authors: Ghoshal, S. S., Junca, S., Parmar, A.
Format: Article
Language:English
Subjects:
Mathematics
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Summary:For the Burgers equation, the entropy solution becomes instantly BV with only $ L^\infty$ initial data. For conservation laws with genuinely nonlinear discontinuous flux, it is well known that the BV regularity of entropy solutions is lost. Recently, this regularity has been proved to be fractional with s = 1/2. Moreover, for less nonlinear flux the solution has still a fractional regularity 0 < s ≤ 1/2. The resulting general rule is the regularity of entropy solutions for a discontinuous flux is less than for a smooth flux. In this paper, an optimal geometric condition on the discontinuous flux is used to recover the same regularity as for the smooth flux with the same kind of non-linearity.
ISSN:0036-1410
1095-7154
DOI:10.1137/23M1604199