## Abstract and Applied Analysis

### The Cauchy Problem for a Fifth-Order Dispersive Equation

#### 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 ${H}^{s}(\mathbf{R})$ with $s\ge 1/4$. We also establish the ill-posedness for the initial data in ${H}^{s}(\mathbf{R})$ with $s<1/4$. Thus, the regularity requirement for the fifth-order dispersive equations $s\ge 1/4$ is sharp.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 404781, 8 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412278800

Digital Object Identifier
doi:10.1155/2014/404781

Mathematical Reviews number (MathSciNet)
MR3191040

Zentralblatt MATH identifier
07022326

#### Citation

Wang, Hongjun; Liu, Yongqi; Chen, Yongqiang. The Cauchy Problem for a Fifth-Order Dispersive Equation. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 404781, 8 pages. doi:10.1155/2014/404781. https://projecteuclid.org/euclid.aaa/1412278800

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