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

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

作　　者：孟志英 殷朝阳[1,2] Meng Zhiying;Yin Zhaoyang(Department of Mathematics,Sun Yat-sen University,Guangzhou 510275;School of Science,Shenzhen Campus of Sun Yat-sen University,Guangdong Shenzhen 518107)

机构地区：[1]中山大学数学学院,广州510275 [2]中山大学理学院,广东深圳518107

出　　处：《数学物理学报（A辑）》2024年第6期1537-1549,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(12171493)。

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(Gσ)中的整体Gevrey正则性,其中σ≥1.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 Gσwithσ≥1 in time.

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 

分 类 号：O175.27[理学—数学]