Well-posedness and persistence properties for the Novikov equation

Recently, Novikov found a new integrable equation (we call it the Novikov equation in this paper), which has nonlinear terms that are cubic, rather than quadratic, and admits peaked soliton solutions (peakons). Firstly, we prove that the Cauchy problem for the Novikov equation is locally well-posed in the Besov spaces B2,rs (which generalize the Sobolev spaces Hs) with the critical index s=32. Then, well-posedness in Hs with s>32, is also established by applying Kato's semigroup theory. Finally, we present two results on the persistence properties of the strong solution for the Novikov equation.