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
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