THE PERIODIC CAUCHY PROBLEM FOR THE 2-COMPONENT CAMASSA-HOLM SYSTEM

被引：0
|
作者：
Thompson, Ryan C. [1 ]
机构：
[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA
来源：
DIFFERENTIAL AND INTEGRAL EQUATIONS | 2013年 / 26卷 / 1-2期
关键词：
SHALLOW-WATER EQUATION; BLOW-UP PHENOMENA; WELL-POSEDNESS; SOLUTION MAP; NONUNIFORM DEPENDENCE; CONTINUITY PROPERTIES; GEODESIC-FLOW; MODEL;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For Sobolev exponent s > 3/2, it is shown that the data-to-solution map for the 2-component Camassa-Holm system is continuous from H-s x Hs-1(T) into C([0, T]; H-s x Hs-1(T)) but not uniformly continuous. The proof of non-uniform dependence on the initial data is based on the method of approximate solutions, delicate commutator and multiplier estimates, and well-posedness results for the solution and its lifespan. Also, the solution map is Holder continuous if the H-s x Hs-1(T) norm is replaced by an H-r x Hr-1(T) norm for 0 <= r < s.
引用
收藏
页码：155 / 182
页数：28
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