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

Access to Document

10.1016/j.jmaa.2010.02.023

Cite this

@article{f2cb54116e7a4b81a4a56936f5a31df8,

title = "Sharp local well-posedness for a fifth-order shallow water wave equation",

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.",

keywords = "Bourgain space, Dispersive equation, Initial value problem, Local well-posedness",

author = "Wengu Chen and Zihua Guo and Zeping Liu",

year = "2010",

month = sep,

doi = "10.1016/j.jmaa.2010.02.023",

language = "English",

volume = "369",

pages = "133--143",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Elsevier",

number = "1",

}

TY - JOUR

T1 - Sharp local well-posedness for a fifth-order shallow water wave equation

AU - Chen, Wengu

AU - Guo, Zihua

AU - Liu, Zeping

PY - 2010/9

Y1 - 2010/9

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/77952582058

U2 - 10.1016/j.jmaa.2010.02.023

DO - 10.1016/j.jmaa.2010.02.023

M3 - Article

AN - SCOPUS:77952582058

SN - 0022-247X

VL - 369

SP - 133

EP - 143

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Cite this