具有弱耗散项的 Camassa-Holm 方程的解析性和整体 Gevrey 正则性

摘要/Abstract

摘要：

该文主要研究了具有弱耗散项的 Camassa-Holm 的柯西问题在 Sobolev-Gevrey 空间的适定性. 首先, 证明了该方程的局部解析性和 Gevrey 正则性. 其次, 探究了解映射的连续性. 最后, 证明了解在 Gevrey 类 ($G_{\sigma}$) 中的整体 Gevrey 正则性, 其中 $\sigma \geq 1$.

关键词: 具有弱耗散项的 Camassa-Holm 方程, 解析性, Gevrey 类, 整体 Gevrey 正则性

Abstract:

This article mainly studies the well posedness of the Cauchy problem of a weakly dissipative Camassa-Holm equation in Sobolev-Gevrey spaces. Firstly, we demonstrate the local Gevrey regularity and analyticity of this equation. Then, we discuss the continuity of the data-to-solution map. Finally, we obtain the global Gevrey regularity of this system in Gevrey class $G_{\sigma}$ with $\sigma\geq 1$ in time.

Key words: A weakly dissipative Camassa-Holm equation, Analyticity, Gevrey class, Global Gevrey regularity

中图分类号:

O175.27

孟志英, 殷朝阳. 具有弱耗散项的 Camassa-Holm 方程的解析性和整体 Gevrey 正则性[J]. 数学物理学报, 2024, 44(6): 1537-1549.

Meng Zhiying, Yin Zhaoyang. Global Gevrey Regularity and Analyticity of a Weakly Dissipative Camassa-Holm Equation[J]. Acta mathematica scientia,Series A, 2024, 44(6): 1537-1549.

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