#### Vol. 6, No. 8, 2013

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
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