Title

Global well-posedness and scattering for the defocusing energy-supercritical cubic nonlinear wave equation

Document Type

Article

Publication Date

9-15-2012

Abstract

In this paper, we consider the defocusing cubic nonlinear wave equation u -δu+|u| u=0 in the energy-supercritical regime, in dimensions d≥6, with no radial assumption on the initial data. We prove that if a solution satisfies an a priori bound in the critical homogeneous Sobolev space throughout its maximal interval of existence, that is, u∈Lt∞(Ḣxsc×Ḣxsc-1), then the solution is global and it scatters. Our analysis is based on the methods of the recent works of Kenig and Merle (2008) [21] and Killip and Visan (2010) [26,27] treating the energy-supercritical nonlinear Schrödinger and wave equations. © 2012 Elsevier Inc. tt 2

Publication Source (Journal or Book title)

Journal of Functional Analysis

First Page

1609

Last Page

1660

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