Revista Matemática Iberoamericana

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Volume 19, Issue 1, 2003, pp. 161–177
DOI: 10.4171/RMI/341

Published online: 2003-04-30

On global solutions to a defocusing semi-linear wave equation

Isabelle Gallagher[1] and Fabrice Planchon[2]

(1) École Polytechnique, Palaiseau, France
(2) Institut Galilée, Université Paris 13, Villetaneuse, France

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]).

Keywords: Wave equation, global solution

Gallagher Isabelle, Planchon Fabrice: On global solutions to a defocusing semi-linear wave equation. Rev. Mat. Iberoam. 19 (2003), 161-177. doi: 10.4171/RMI/341