Strong time regularity and decay of $L^\infty$ solutions to $2\times 2$ systems of conservation laws
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915408270852096 |
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| author | Talamini, Luca |
| author_facet | Talamini, Luca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong time regularity and decay of $L^\infty$ solutions to $2\times 2$ systems of conservation laws Talamini, Luca Analysis of PDEs 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. |
| title | Strong time regularity and decay of $L^\infty$ solutions to $2\times 2$ systems of conservation laws |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.18427 |