On the Cauchy problem for a generalized Degasperis-Procesi equation

ABSTRACT

We first establish the local well-posedness for a generalized Degasperis-Procesi equation in nonhomogeneous Besov spaces. Then we present a global existence result for the equation. Moreover, we obtain a blow-up criteria and provide a sufficient condition for strong solutions to blow up in finite time.

COMMUNICATED BY:

• Adrian Constantin

KEYWORDS:

• A generalized Degasperis-Procesi equation
• local well-posedness
• global existence
• bseov spaces
• blow-up

MATEMATICS SUBJECT CLASSIFICATION 2000:

• 35G25
• 35L05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by NNSFC [grant number 11671407], FDCT [grant number 098/2013/A3], Guangdong Special Support Program [grant number 8-2015], and the key project of NSF of Guangdong province [grant number 2016A03031104].