Global well-posedness for the periodic Novikov equation with cubic nonlinearity. Issue 2 (1st February 2016) - Wu, Xinglong; Guo, Boling
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.