On the energy subcritical, nonlinear wave equation in ℝ3 with radial data

Shen, Ruipeng

doi:10.2140/apde.2013.6.1929

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On the energy subcritical, nonlinear wave equation in $\mathbb{R}^3$ with radial data

Ruipeng Shen

Vol. 6 (2013), No. 8, 1929–1987

DOI: 10.2140/apde.2013.6.1929

Abstract

In this paper, we consider the wave equation in 3-dimensional space with an energy-subcritical nonlinearity, either in the focusing or defocusing case. We show that any radial solution of the equation which is bounded in the critical Sobolev space is globally defined in time and scatters. The proof depends on the compactness/rigidity argument, decay estimates for radial, “compact” solutions, gain of regularity arguments and the “channel of energy” method.

Keywords

wave equation, scattering, nonlinear, energy subcritical

Mathematical Subject Classification 2010

Primary: 35L15, 35L71

Milestones

Received: 22 October 2012

Accepted: 5 August 2013

Published: 20 April 2014

Authors

Ruipeng Shen
Department of Mathematics and Statistics McMaster University 1280 Main Street West Hamilton, Ontario L8S4K1 Canada

Vol. 6, No. 8, 2013