Scholarlink

<p>In this paper, we prove that the continuity of the solution for the generalized Camassa-Holm equation cannot be improved to the Hölder continuity. To be precise, the solution of the generalized Camassa–Holm equation belongs to <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\mathcal {C}([0,T];B^s_{p,r})\)</EquationSource></InlineEquation> but not to <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(\mathcal {C}^\alpha ([0,T];B^s_{p,r})\)</EquationSource></InlineEquation> with any <InlineEquation ID="IEq3"><EquationSource Format="TEX">\(\alpha \in (0,1)\)</EquationSource></InlineEquation>.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Loss of Hölder Regularity for Solutions of the Generalized Camassa-Holm Equation in Besov Spaces

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年6月18日

查看全文
  • Guorong Qu,
  • Jianzhong Lu,
  • Fulai Chen,
  • Xing Wu

摘要

In this paper, we prove that the continuity of the solution for the generalized Camassa-Holm equation cannot be improved to the Hölder continuity. To be precise, the solution of the generalized 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 \(\alpha \in (0,1)\).