Vol. 6, No. 8, 2013

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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

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.

wave equation, scattering, nonlinear, energy subcritical
Mathematical Subject Classification 2010
Primary: 35L15, 35L71
Received: 22 October 2012
Accepted: 5 August 2013
Published: 20 April 2014
Ruipeng Shen
Department of Mathematics and Statistics
McMaster University
1280 Main Street West
Hamilton, Ontario L8S4K1