Journal of Nonlinear Mathematical Physics

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Volume 18, Issue 4, December 2011, Pages 541 - 556

On a Periodic 2-Component Camassa–Holm Equation with Vorticity

Authors
Qiaoyi Hu
Department of Mathematics, South China Agricultural University, 510642 Guangzhou, China,huqiaoyi@scau.edu.cn
Received 9 April 2011, Accepted 30 May 2011, Available Online 7 January 2021.
DOI
10.1142/S1402925111001787How to use a DOI?
Keywords
A periodic 2-component Camassa–Holm equation; vorticity; global existence; blow-up; blow-up rate
Abstract

We consider a periodic 2-component Camassa–Holm equation with vorticity in the paper. We first give the local well-posedness and the blow-up criterion for strong solutions to the equation in the Sobolev space Hs, s>32 . We then present a global existence result for strong solutions to the equation. We finally obtain several blow-up results and the blow-up rate of strong solutions to the equation. We finally examine the propagation behaviour of compactly supported solutions to the equation. The obtained results cover and improve the earlier results for a periodic 2-component Camssa–Holm equation without vorticity.

Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - 4
Pages
541 - 556
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925111001787How to use a DOI?
Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

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TY  - JOUR
AU  - Qiaoyi Hu
PY  - 2021
DA  - 2021/01/07
TI  - On a Periodic 2-Component Camassa–Holm Equation with Vorticity
JO  - Journal of Nonlinear Mathematical Physics
SP  - 541
EP  - 556
VL  - 18
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001787
DO  - 10.1142/S1402925111001787
ID  - Hu2021
ER  -