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.
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页码：435 / 461
页数：27
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