Preprint

Inserted: 24 jul 2025
Last Updated: 24 jul 2025

Year: 2025

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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• Time_regularity_2x2.pdf