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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 404781, 8 pages
http://dx.doi.org/10.1155/2014/404781
Research Article

The Cauchy Problem for a Fifth-Order Dispersive Equation

College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, China

Received 21 January 2014; Accepted 8 February 2014; Published 27 March 2014

Academic Editor: Changsen Yang

Copyright © 2014 Hongjun Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is devoted to studying the Cauchy problem for a fifth-order equation. We prove that it is locally well-posed for the initial data in the Sobolev space with . We also establish the ill-posedness for the initial data in with . Thus, the regularity requirement for the fifth-order dispersive equations is sharp.