The Cauchy problem for the modified Kawahara equation in Sobolev spaces with low regularity

This paper is concerned with the Cauchy problem of the modified Kawahara equation. By using the Fourier restriction norm method introduced by Bourgain, and using the II-method as well as the L2L2 conservation law, we prove that the modified Kawahara equation is globally well-posed for the initial data in the Sobolev space Hs(R) with s>−322.