Well-posedness and persistence properties for the Novikov equation (Q630581)

The authors prove that the Cauchy problem for the Novikov equation \[ \partial_tu-\partial_t\partial_x^2u+4u^2\partial_xu=3u\partial_xu\partial_x^2u+u^2\partial_x^3u,\quad u(0)=u_0, \] is locally well-posed in the Besov spaces \(B_{2,r}^{3/2}\) and in the Sobolev spaces \(H^s\) with \(s>3/2\). Some persistence properties for the strong solution of the above problem are also established.