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arXiv · 2207.12979

On optimal regularity estimates for finite-entropy solutions of scalar conservation laws

Xavier Lamy·Andrew Lorent·Guanying Peng
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Abstract

We consider finite-entropy solutions of scalar conservation laws $u_t +a(u)_x =0$, that is, bounded weak solutions whose entropy productions are locally finite Radon measures. Under the assumptions that the flux function $a$ is strictly convex (with possibly degenerate convexity) and $a''$ forms a doubling measure, we obtain a characterization of finite-entropy solutions in terms of an optimal regularity estimate involving a cost function first used by Golse and Perthame.

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Xavier Lamy, Andrew Lorent, Guanying Peng. 2022-07-26. On optimal regularity estimates for finite-entropy solutions of scalar conservation laws. https://arxiv.org/abs/2207.12979

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