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<p>We consider <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\textbf{L}^\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="bold">L</mi> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation> solutions to <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(2\times 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>×</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(C^0(\mathbb {R}^+,; \textbf{L}^1_{loc}(\mathbb {R}))\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>C</mi> <mn>0</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mo>+</mo> </msup> <mo>,</mo> <mo>;</mo> <msubsup> <mi mathvariant="bold">L</mi> <mrow> <mi mathvariant="italic">loc</mi> </mrow> <mn>1</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Our second result establishes a dispersive-type decay estimate for vanishing viscosity solutions. Both results are unified by the use of a kinetic formulation.</p>

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Strong time regularity and decay of \({\textbf{L}}^\infty \) solutions to \(2\times 2\) systems of conservation laws

  • 期刊论文

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  • 发表日期：

    2026年4月1日

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  • Luca Talamini

摘要

We consider \(\textbf{L}^\infty \) L ∞ solutions to \(2\times 2\) 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 \(C^0(\mathbb {R}^+,; \textbf{L}^1_{loc}(\mathbb {R}))\) 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.