Global well-posedness for the periodic Novikov equation with cubic nonlinearity

Abstract

This paper is devoted to the study of the Cauchy problem to the periodic Novikov equation. Firstly, the local well-posedness for the equation is established. Secondly, we give the precise blow-up criterion, conservation laws, and prove that the equation has global strong solutions in time, if the initial potential does not change sign on . Thirdly, with the initial potential satisfying the sign conditions, we show the existence of global weak solutions in time. Moreover, the uniqueness of global solution is addressed.

Keywords:

• the periodic Novikov equation
• well-posedness
• blow-up scenario
• conservation laws
• global solutions
• Peakon solutions

AMS Subject Classifications:

• 35G25
• 35L05

Acknowledgements

The authors thank the references for their valuable comments and constructive suggestions.

Additional information

Funding

This work was partially supported by CPSF [grant number 2013T60086] and National Natural Science Foundation of China (NSFC) [grant number 11401122].