On the Cauchy problem of generalized Fokas–Olver–Resenau–Qiao equation

ABSTRACT

In this paper, we study the Cauchy problem of the generalized Fokas–Olver–Resenau–Qiao equation. Firstly, by means of transport equation and Littlewood–Paley theory, we obtain the local well-posedness of the equation in the nonhomogeneous Besov space with , . Secondly, we consider the local well-posedness in the critical space and show the continuality of the data-to-solution mapping. Thirdly, two blow-up criterion are addressed.

KEYWORDS:

• Generalized Fokas–Olver–Resenau–Qiao equation
• Besov space
• Cauchy problem
• well-posedness
• blow-up

AMS SUBJECT CLASSIFICATIONS:

• 35Q53
• 35G25
• 35A01

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the NSFC (Tianyuan fund for Mathematics, [grant number 11526062]), by NSFC [grant number 11571118].