Global well-posedness of the Cauchy problem of the fifth-order shallow water equation

被引：18
|
作者：
Wang, Hua [1 ]
Cui, Shangbin [1 ]
机构：
[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2006年 / 230卷 / 02期
基金：
中国国家自然科学基金;
关键词：
fifth-order shallow water equation; global well-posedness; I-method;
D O I：
10.1016/j.jde.2006.04.008
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
By using the I-method, we prove that the Cauchy problem of the fifth-order shallow water equation partial derivative(t)u - partial derivative(2)(X) partial derivative(t)u + partial derivative(3)(x)u + 3u partial derivative(x)u - 2 partial derivative(x)u partial derivative(2)(x)u - u partial derivative(3)(x)u - partial derivative(5)(x)u = 0 is globally well-posed in the Sobolev space H-s (R) provided s > (5 root 7- 10)/4. (c) 2006 Elsevier Inc. All rights reserved.
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页码：600 / 613
页数：14
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