Revista Matemática Iberoamericana

On global solutions to a defocusing semi-linear wave equation

Isabelle Gallagher and Fabrice Planchon

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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 $\dot{H}^{s}$ 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])

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Rev. Mat. Iberoamericana, Volume 19, Number 1 (2003), 161-177.

First available in Project Euclid: 31 March 2003

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Primary: 35L70: Nonlinear second-order hyperbolic equations 35L05: Wave equation

Wave equation Global solution


Gallagher, Isabelle; Planchon, Fabrice. On global solutions to a defocusing semi-linear wave equation. Rev. Mat. Iberoamericana 19 (2003), no. 1, 161--177.

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