Open Access
March, 2003 On global solutions to a defocusing semi-linear wave equation
Isabelle Gallagher, Fabrice Planchon
Rev. Mat. Iberoamericana 19(1): 161-177 (March, 2003).


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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Isabelle Gallagher. Fabrice Planchon. "On global solutions to a defocusing semi-linear wave equation." Rev. Mat. Iberoamericana 19 (1) 161 - 177, March, 2003.


Published: March, 2003
First available in Project Euclid: 31 March 2003

zbMATH: 1036.35142
MathSciNet: MR1993418

Primary: 35L05 , 35L70

Keywords: global solution , wave equation

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.19 • No. 1 • March, 2003
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