The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces

Abstract

This paper is concerned with the periodic boundary value problem for a quasilinear evolution equation of the following type:∂tu+f(u)∂xu+F(u)=0,x∈T=R/2πZ,t∈R+. Under some conditions, we prove that this equation is locally well-posed in Besov spaceBp,rs(T). Furthermore, we study the continuity of the solution map for this equation inB2,rs(T). Our work improves some earlier results.