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
Recommended Citation
Bulut, A. (2012). Global well-posedness and scattering for the defocusing energy-supercritical cubic nonlinear wave equation. Journal of Functional Analysis, 263 (6), 1609-1660. https://doi.org/10.1016/j.jfa.2012.06.001