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Wang, Hongjun; Liu, Yongqi; Chen, Yongqiang

The Cauchy problem for a fifth-order dispersive equation. (English) Zbl 1472.35340

Abstr. Appl. Anal. 2014, Article ID 404781, 8 p. (2014).
Summary: 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 \(H^s(\mathbb{R})\) with \(s \geq 1 / 4\). We also establish the ill-posedness for the initial data in \(H^s(\mathbb{R})\) with \(s < 1 / 4\). Thus, the regularity requirement for the fifth-order dispersive equations \(s \geq 1 / 4\) is sharp.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B65 Smoothness and regularity of solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35R25 Ill-posed problems for PDEs

Keywords:

fifth-order equation
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References:

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