The Navier-Stokes equations in the critical Morrey-Campanato space.

P. G. Lemarié-Rieusset

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We prove that the 3D cubic defocusing semi-linear wave equation is globally well-posed for data in the Sobolev space Hs 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]).