Sharp local well-posedness for a fifth-order shallow water wave equation

Wengu Chen; Zihua Guo; Zeping Liu

doi:10.1016/j.jmaa.2010.02.023

Sharp local well-posedness for a fifth-order shallow water wave equation

Wengu Chen, Zihua Guo, Zeping Liu

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

In this paper we prove that the already-established local well-posedness in the range s>-5/4 of the Cauchy problem with an initial H^s(R) data for a fifth-order shallow water wave equation is extendable to s=-5/4 by using the F^s space. This is sharp in the sense that the ill-posedness in the range s<-5/4 of this initial value problem is already known.

Original language	English
Pages (from-to)	133-143
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	369
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2010.02.023
Publication status	Published - Sept 2010
Externally published	Yes

Keywords

Bourgain space
Dispersive equation
Initial value problem
Local well-posedness

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10.1016/j.jmaa.2010.02.023

Cite this

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abstract = "In this paper we prove that the already-established local well-posedness in the range s>-5/4 of the Cauchy problem with an initial Hs(R) data for a fifth-order shallow water wave equation is extendable to s=-5/4 by using the Fs space. This is sharp in the sense that the ill-posedness in the range s<-5/4 of this initial value problem is already known.",

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AU - Guo, Zihua

AU - Liu, Zeping

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AB - In this paper we prove that the already-established local well-posedness in the range s>-5/4 of the Cauchy problem with an initial Hs(R) data for a fifth-order shallow water wave equation is extendable to s=-5/4 by using the Fs space. This is sharp in the sense that the ill-posedness in the range s<-5/4 of this initial value problem is already known.

KW - Bourgain space

KW - Dispersive equation

KW - Initial value problem

KW - Local well-posedness

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JF - Journal of Mathematical Analysis and Applications

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ER -

Sharp local well-posedness for a fifth-order shallow water wave equation

Abstract

Keywords

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