This analysis demonstrates regularity and decay of L-infinity solutions in nonlinear conservation laws, suggesting important implications for mathematical modeling.
We consider L^∞ L ∞ solutions to 2× 2 2 × 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 C⁰(R⁺,; L¹loc(R)) C 0 ( R + , ; L loc 1 ( 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 (2026) studied this question.
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