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2013 On the energy subcritical, nonlinear wave equation in $\mathbb{R}^3$ with radial data
Ruipeng Shen
Anal. PDE 6(8): 1929-1987 (2013). 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.

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Ruipeng Shen. "On the energy subcritical, nonlinear wave equation in $\mathbb{R}^3$ with radial data." Anal. PDE 6 (8) 1929 - 1987, 2013. https://doi.org/10.2140/apde.2013.6.1929

Information

Received: 22 October 2012; Accepted: 5 August 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1295.35330
MathSciNet: MR3198589
Digital Object Identifier: 10.2140/apde.2013.6.1929

Subjects:
Primary: 35L15 , 35L71

Keywords: energy subcritical , nonlinear , scattering , wave equation

Rights: Copyright © 2013 Mathematical Sciences Publishers

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Vol.6 • No. 8 • 2013
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