On global solutions to a defocusing semi-linear wave equation

On global solutions to a defocusing semi-linear wave equation

Isabelle Gallagher and Fabrice Planchon

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

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])

Primary Subjects: 35L70, 35L05

Keywords: Wave equation; Global solution

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rmi/1049123083
Mathematical Reviews number (MathSciNet): MR1993418
Zentralblatt MATH identifier: 1036.35142

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