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Well-posedness, blowup, and global existence for an integrable shallow water equation

Yin, Zhaoyang LU (2004) In Discrete and Continuous Dynamical Systems. Series A 11(2-3). p.393-411
Abstract
We establish the local well-posedness for a recently derived model that combines the linear dispersion of Korteweg-de Veris equation with the nonlinear/nonlocal dispersion of the Camassa-Holm equation, and we prove that the equation has solutions that exist for indefinite times as well as solutions that blow up in finite time. We also derive an explosion criterion for the equation, and we give a sharp estimate of the existence time for solutions with smooth initial data.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
lower semicontinuity, sharp estimate from below, explosion criterion, global existence, local well-posedness, blowup, peaked solitons
in
Discrete and Continuous Dynamical Systems. Series A
volume
11
issue
2-3
pages
393 - 411
publisher
American Institute of Mathematical Sciences
external identifiers
  • wos:000223883000007
  • scopus:4944227680
ISSN
1553-5231
language
English
LU publication?
yes
id
15e0a3e0-fc1b-4f6f-ac41-2312f12d5cda (old id 267173)
alternative location
http://aimsciences.org/journals/dcdsA/online.jsp
date added to LUP
2007-11-07 08:30:09
date last changed
2017-07-09 04:28:17
@article{15e0a3e0-fc1b-4f6f-ac41-2312f12d5cda,
  abstract     = {We establish the local well-posedness for a recently derived model that combines the linear dispersion of Korteweg-de Veris equation with the nonlinear/nonlocal dispersion of the Camassa-Holm equation, and we prove that the equation has solutions that exist for indefinite times as well as solutions that blow up in finite time. We also derive an explosion criterion for the equation, and we give a sharp estimate of the existence time for solutions with smooth initial data.},
  author       = {Yin, Zhaoyang},
  issn         = {1553-5231},
  keyword      = {lower semicontinuity,sharp estimate from below,explosion criterion,global existence,local well-posedness,blowup,peaked solitons},
  language     = {eng},
  number       = {2-3},
  pages        = {393--411},
  publisher    = {American Institute of Mathematical Sciences},
  series       = {Discrete and Continuous Dynamical Systems. Series A},
  title        = {Well-posedness, blowup, and global existence for an integrable shallow water equation},
  volume       = {11},
  year         = {2004},
}