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

页码：155 / 182

页数：28

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