GLOBAL WELL-POSEDNESS FOR THE KAWAHARA EQUATION WITH LOW REGULARITY

We consider the global well-posedness for the Cauchy problem of the Kawahara equation which is one of fifth order KdV type equations. We first establish the local well-posedness in a more suitable function space for the global well-posedness by a variant of the Fourier restriction norm method introduced by Bourgain. Next, we extend this local solution globally in time by the I-method. In the present paper, we can apply the I-method to the modified Bourgain space in which the structure of the nonlinear term is reflected.