On global solutions to a defocusing semi-linear wave equation

Abstract

We prove that the 3D cubic defocusing semi-linear wave equation is globally well-posed for data in the Sobolev space Ḣs where s > 3/4. This result was obtained in [11] following Bourgain's method ([3]). We present here a different and somewhat simpler argument, inspired by previous work on the Navier-Stokes equations ([4, 7]).