Optimal regularity for all time for entropy solutions of conservation laws in $BV^s$
| Autor: | Ghoshal, Shyam Sundar, Guelmame, Billel, Jana, Animesh, Junca, Stéphane |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Nonlinear Differ. Equ. Appl., Volume 27, Article number 46 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00030-020-00649-5 |
| Popis: | This paper deals with the optimal regularity for entropy solutions of conservation laws. For this purpose, we use two key ingredients: (a) fine structure of entropy solutions and (b) fractional $BV$ spaces. We show that optimality of the regularizing effect for the initial value problem from $L^\infty$ to fractional Sobolev space and fractional $BV$ spaces is valid for all time. Previously, such optimality was proven only for a finite time, before the nonlinear interaction of waves. Here for some well-chosen examples, the sharp regularity is obtained after the interaction of waves. Moreover , we prove sharp smoothing in $BV^s$ for a convex scalar conservation law with a linear source term. Next, we provide an upper bound of the maximal smoothing effect for nonlinear scalar multi-dimensional conservation laws and some hyperbolic systems in one or multi-dimension. Comment: Published in NoDEA in 2020 |
| Databáze: | arXiv |
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