Local and global analyticity for the μ-Novikov equation

ABSTRACT

Considered herein is the Cauchy problem of the μ-Novikov equation in the periodic setting. We first prove the existence and uniqueness of local analytic solution of this problem by using the autonomous Ovsyannikov theorem. Then based on the local well-posedness and the blow-up scenario of this problem, the existence of the global solution is established. Finally, we obtain the global-in-time analyticity of the solution of this problem.

KEYWORDS:

• μ-Novikov equation
• local analytic solution
• blow-up scenario
• global existence
• global analyticity

(2020) AMS SUBJECT CLASSIFICATIONS:

• 35B30
• 35G25

Disclosure statement

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

Additional information

Funding

The work of Fu is supported in part by the National Natural Science Foundation of China [grant number 11471259] and the Natural Science Foundation of Shaanxi province [grant numbers 2019JM-007,2020JC-37].