Abstract
We prove that the 3D cubic defocusing semi-linear wave equation is globally well-posed for data in the Sobolev space $\dot{H}^{s}$ where $s>3/4$. This result was obtained in [Kenig-Ponce-Vega, 2000] following Bourgain's method ([Bourgain, 1998]). We present here a different and somewhat simpler argument, inspired by previous work on the Navier-Stokes equations ([Calderon, 1990], [Gallagher-Planchon, 2002])
Citation
Isabelle Gallagher. Fabrice Planchon. "On global solutions to a defocusing semi-linear wave equation." Rev. Mat. Iberoamericana 19 (1) 161 - 177, March, 2003.
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