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