Lower order regularity for the generalized Camassa–Holm equation

Abstract

This paper deals with the Cauchy problem for the generalized Camassa–Holm equation. The existence of weak solutions for the generalized Camassa–Holm equation in lower order Sobolev space with is obtained.

Keywords:

• Lower order regularity
• Camassa–Holm equation
• weak solutions
• local well-posedness

AMS Subject Classifications:

• 35Q35
• 35Q51

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by NSF of China [grant number 11401050], partially supported by Program for Innovation Team at Yangtze Normal University.