A note on the solution map for the periodic multi-dimensional Camassa-Holm-type system

被引：2

作者：

Fu, Ying ^{[1
,2
]}

Wang, Haiquan ^{[3
]}

机构：

[1] Northwest Univ, Sch Math, Xian 710127, Peoples R China

[2] Northwest Univ, Ctr Nonlinear Studies, Xian 710127, Peoples R China

[3] Taiyuan Univ Technol, Coll Math, Taiyuan 030024, Peoples R China

来源：

MONATSHEFTE FUR MATHEMATIK | 2022年 / 197卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Non-uniform dependence; Periodic multi-dimensional Camassa-Holm system; Besov spaces; Approximate solutions; SHALLOW-WATER EQUATION; NONUNIFORM DEPENDENCE; WELL-POSEDNESS; GLOBAL EXISTENCE; BREAKING WAVES; CAUCHY-PROBLEM; INITIAL DATA;

D O I：

10.1007/s00605-021-01615-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Considered in this paper is the initial value problem of periodic multi-dimensional Camassa-Holm-type system. It is shown that the solution map of this problem is not uniformly continuous in Besov spaces B-2,1(1+d/2)(T-d) x B-2,1(d/2)(T-d) with d is an element of Z(+), d >= 1. Based on the local well-posedness results, the method of approximate solutions is utilized.

引用

页码：435 / 461

页数：27

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