GLOBAL WELL-POSEDNESS FOR A FIFTH-ORDER SHALLOW WATER EQUATION ON THE CIRCLE

被引：0

作者：

李用声

杨兴雨

机构：

[1] DepartmentofMathematics,SouthChinaUniversityofTechnology

来源：

Acta Mathematica Scientia | 2011年 / 31卷 / 04期

关键词：

shallow water equation; periodic initial value problem; global well-posedness; I-method; almost conservation law;

D O I：

暂无

中图分类号：

O175.8 [边值问题];

学科分类号：

070104 ;

摘要：

The periodic initial value problem of a fifth-order shallow water equation t u 2 x t u + 3 x u 5 x u + 3u x u 2 x u 2 x u u 3 x u = 0 is shown to be globally well-posed in Sobolev spaces˙ H s (T) for s > 2/3 by I-method. For this equation lacks scaling invariance, we first reconsider the local result and pay special attention to the relationship between the lifespan of the local solution and the initial data, and then prove the almost conservation law, and finally obtain the global well-posedness by an iteration process.

引用

页码：1303 / 1317

页数：15

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