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Open Access Research

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

Hongjun Wang1* and Yan Zheng2

Author Affiliations

1 College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, 453007, P.R. China

2 Henan Vocational College of Agriculture, Zhengzhou, Henan, 451450, P.R. China

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Boundary Value Problems 2014, 2014:122  doi:10.1186/1687-2770-2014-122

Published: 20 May 2014

Abstract

This paper is devoted to the Cauchy problem for the higher-order dispersive equation <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/122/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/122/mathml/M1">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/122/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/122/mathml/M2">View MathML</a>. The local well-posedness of the associated Cauchy problem is established in Sobolev space <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/122/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/122/mathml/M3">View MathML</a> with <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/122/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/122/mathml/M4">View MathML</a> with the aid of the Fourier restriction norm method.

MSC: 35K30.

Keywords:
Cauchy problem; well-posedness; Sobolev spaces