Well-posedness, blowup, and global existence for an integrable shallow water equation
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/267173
- author
- Yin, Zhaoyang LU
- organization
- publishing date
- 2004
- 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
- 2016-04-01 17:00:38
- date last changed
- 2022-01-28 23:44:43
@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}}, keywords = {{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}}, url = {{http://aimsciences.org/journals/dcdsA/online.jsp}}, volume = {{11}}, year = {{2004}}, }