The failure of H\'{o}lder regularity of solutions for the Camassa--Holm type equation in Besov spaces
| Autor: | Li, Jinlu, Yu, Yanghai, Zhu, Weipeng |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | It is proved that if $u_0\in B^s_{p,r}$ with $s>1+\frac1p, (p,r)\in[1,+\infty]\times[1,+\infty)$ or $s=1+\frac1p, \ (p,r)\in[1,+\infty)\times \{1\}$, the solution of the Camassa--Holm equation belongs to $\mathcal{C}([0,T];B^s_{p,r})$. In the paper, we show that the continuity of the solution can not be improved to the H\"{o}lder continuity. Precisely speaking, the solution of the Camassa--Holm equation belongs to $\mathcal{C}([0,T];B^s_{p,r})$ but not to $\mathcal{C}^\alpha([0,T];B^s_{p,r})$ with any $\alpha\in(0,1)$. Comment: arXiv admin note: substantial text overlap with arXiv:2112.14104 |
| Databáze: | arXiv |
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