Publication Cover
Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 4
232
Views
7
CrossRef citations to date
0
Altmetric
Articles

On a generalized Camassa–Holm equation with the flow generated by velocity and its gradient

&
Pages 679-701 | Received 13 Dec 2015, Accepted 03 Feb 2016, Published online: 23 Feb 2016
 

Abstract

In this paper, we consider a generalized Camassa–Holm equation with the flow generated by the vector field and its gradient. We first establish the local well-posedness of equation in the sense of Hadamard in both critical Besov spaces and supercritical Besov spaces. Then we gain a blow-up criterion. Under a sign condition we reach the sign-preserved property and a precise blow-up criterion. Applying this precise criterion we finally present two blow-up results and the precise blow-up rate for strong solutions to equation.

AMS Subject Classifications:

Acknowledgements

We thank the referee for the valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by NNSFC [grant number 11271382]; RFDP [grant number 20120171110014]; MSTDF [grant number 098/2013/A3]; Guangdong Special Support Program [grant number 8-2015].

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.