The Cauchy Problem of the Modified Kawahara Equation

Abstract

In this paper, we consider the local and global solutions for the modified Kawahara equation with data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data. The techniques to be used are adapted from Kato's smoothing effect and the maximal function (in time) estimate for the free Kawahara operator e^{-ϒ^{t∂^5_x}}.