Strong time regularity and decay of $L^\infty$ solutions to $2\times 2$ systems of conservation laws

Luca Talamini

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arXiv · 2507.18427

Strong time regularity and decay of $L^\infty$ solutions to $2\times 2$ systems of conservation laws

Luca Talamini

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Abstract

We consider $\mathbf L^\infty$ solutions to $2\times 2$ systems of conservation laws. For genuinely nonlinear systems we prove that finite entropy solutions (in particular entropy solutions, if a uniformly convex entropy exists) belong to $C^0(\mathbb R^+; \mathbf L^1_{loc}(\mathbb R))$. Our second result establishes a dispersive-type decay estimate for vanishing viscosity solutions. Both results are unified by the use of a kinetic formulation.

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Luca Talamini. 2025-07-24. Strong time regularity and decay of $L^\infty$ solutions to $2\times 2$ systems of conservation laws. https://arxiv.org/abs/2507.18427

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