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

Abstract

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

CLC Number:

O175.27

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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References 49

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Global Gevrey Regularity and Analyticity of a Weakly Dissipative Camassa-Holm Equation

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