On optimal regularity estimates for finite-entropy solutions of scalar conservation laws
We consider finite-entropy solutions of scalar conservation laws $u_t +a(u)_x =0$, that is, bounded weak solutions whose entropy productions are locally finite Radon measures. Under the assumptions that the flux function $a$ is strictly convex (with possibly degenerate convexity) and $a^{\prime \pri...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-03-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.427/ |
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| author | Lamy, Xavier Lorent, Andrew Peng, Guanying |
| author_facet | Lamy, Xavier Lorent, Andrew Peng, Guanying |
| author_sort | Lamy, Xavier |
| collection | DOAJ |
| description | We consider finite-entropy solutions of scalar conservation laws $u_t +a(u)_x =0$, that is, bounded weak solutions whose entropy productions are locally finite Radon measures. Under the assumptions that the flux function $a$ is strictly convex (with possibly degenerate convexity) and $a^{\prime \prime }$ forms a doubling measure, we obtain a characterization of finite-entropy solutions in terms of an optimal regularity estimate involving a cost function first used by Golse and Perthame. |
| format | Article |
| id | doaj-art-a370e13c0b7247d3b991853df680ba5d |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-a370e13c0b7247d3b991853df680ba5d2025-02-07T11:07:00ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-03-01361G359960810.5802/crmath.42710.5802/crmath.427On optimal regularity estimates for finite-entropy solutions of scalar conservation lawsLamy, Xavier0Lorent, Andrew1Peng, Guanying2Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UPSIMT, F-31062 Toulouse Cedex 9, France.Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA.Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, USA.We consider finite-entropy solutions of scalar conservation laws $u_t +a(u)_x =0$, that is, bounded weak solutions whose entropy productions are locally finite Radon measures. Under the assumptions that the flux function $a$ is strictly convex (with possibly degenerate convexity) and $a^{\prime \prime }$ forms a doubling measure, we obtain a characterization of finite-entropy solutions in terms of an optimal regularity estimate involving a cost function first used by Golse and Perthame.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.427/ |
| spellingShingle | Lamy, Xavier Lorent, Andrew Peng, Guanying On optimal regularity estimates for finite-entropy solutions of scalar conservation laws Comptes Rendus. Mathématique |
| title | On optimal regularity estimates for finite-entropy solutions of scalar conservation laws |
| title_full | On optimal regularity estimates for finite-entropy solutions of scalar conservation laws |
| title_fullStr | On optimal regularity estimates for finite-entropy solutions of scalar conservation laws |
| title_full_unstemmed | On optimal regularity estimates for finite-entropy solutions of scalar conservation laws |
| title_short | On optimal regularity estimates for finite-entropy solutions of scalar conservation laws |
| title_sort | on optimal regularity estimates for finite entropy solutions of scalar conservation laws |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.427/ |
| work_keys_str_mv | AT lamyxavier onoptimalregularityestimatesforfiniteentropysolutionsofscalarconservationlaws AT lorentandrew onoptimalregularityestimatesforfiniteentropysolutionsofscalarconservationlaws AT pengguanying onoptimalregularityestimatesforfiniteentropysolutionsofscalarconservationlaws |