The cauchy problem for Kawahara equation in Sobolev spaces with low regularity

摘要

This paper is devoted to studying the initial-value problem of the Kawahara equation. By establishing some crucial bilinear estimates related to the Bourgain spaces X_(s,b)(R~2) introduced by Bourgain and homogeneous Bourgain spaces, which is defined in this paper and using I-method as well as L~2 conservation law, we show that this fifth-order shallow water wave equation is globally well-posed for the initial data in the Sobolev spaces H~s(R) with >-63/58.