The existence of global weak solutions for a generalized Camassa–Holm equation

ABSTRACT

In this paper, we mainly study the Cauchy problem of a generalized Camassa–Holm equation. We prove the existence of global weak solutions for this generalized Camassa–Holm equation by the viscous approximation method.

Keywords:

• A generalized Camassa–Holm equation
• global weak solution
• the viscous approximation method

2000 Mathematics Subject Classifications:

• 35Q53
• 35A01
• 35B44
• 35B65

Acknowledgments

This work was partially supported by NNSFC (No. 11671407 and No. 11801076), FDCT (No. 0091/2018/A3), Guangdong Special Support Program (No. 8-2015) and the key project of NSF of Guangdong Province (No. 2016A030311004).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by NNSFC [grant number 11671407], [grant number 11801076], FDCT [grant number 0091/2018/A3], Guangdong Special Support Program [grant number 8-2015] and the key project of NSF of Guangdong Province [grant number 2016A030311004].