Scattering for radial, bounded solutions of focusing supercritical wave equations
Analysis of PDEs
2012-08-13 v1
Abstract
In this paper, we consider the wave equation in space dimension 3 with an energy-supercritical, focusing nonlinearity. We show that any radial solution of the equation which is bounded in the critical Sobolev space is globally defined and scatters to a linear solution. As a consequence, finite time blow-up solutions have critical Sobolev norm converging to infinity (along some sequence of times). The proof relies on the compactness/rigidity method, pointwise estimates on compact solutions obtained by the two last authors, and channels of energy arguments used by the authors in previous works on the energy-critical equation.
Keywords
Cite
@article{arxiv.1208.2158,
title = {Scattering for radial, bounded solutions of focusing supercritical wave equations},
author = {Thomas Duyckaerts and Carlos Kenig and Frank Merle},
journal= {arXiv preprint arXiv:1208.2158},
year = {2012}
}