The Cauchy problem for a shallow water type equation

被引：23

作者：

Himonas, AA ^{[1
]}

Misiolek, G

机构：

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[2] CALTECH, Dept Math, Notre Dame, IN 46556 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 1998年 / 23卷 / 1-2期

基金：

美国国家科学基金会;

关键词：

Cauchy problem; periodic; Fourier transform; local; global existence;

D O I：

10.1080/03605309808821340

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove existence and uniqueness of local and global solutions of the periodic Cauchy problem for a higher order shallow water type equation under low regularity initial data. Using Fourier analysis we first prove local estimates in appropriate spaces and then use a contraction mapping argument and a conserved norm to get global existence.

引用

页码：123 / 139

页数：17