The Cauchy problem for the seventh-order dispersive equation in Sobolev space

被引：0

作者：

Wang, Hongjun ^{[1
]}

Zheng, Yan ^{[2
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China

[2] Henan Vocat Coll Agr, Zhengzhou 451450, Henan, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2014年

关键词：

Cauchy problem; well-posedness; Sobolev spaces;

D O I：

10.1186/1687-2770-2014-122

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the Cauchy problem for the higher-order dispersive equation u(t) + partial derivative(7)(x)u = partial derivative(2)(x)(u(2)), x, t is an element of R. The local well-posedness of the associated Cauchy problem is established in Sobolev space H-s(R) with s > -7/4 with the aid of the Fourier restriction norm method.

引用

页数：9

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