Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications

Details Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications

2008-10-27

arxiv.org/abs/0810.4834v2

Mathematics

Analysis of PDEs

The new version fixes an error (pointed out by Chengbo Wang) in an incorrect use of the Hardy-Littlewood-Sobolev inequality or

Scientific paper

In this paper we establish optimal pointwise decay estimates for non-dispersive (compact) radial solutions to non-linear wave equations in 3 dimensions, in the energy supercritical range. As an application, we show for the full energy supercritical range, in the defocusing case, that if the scale invariant Sobolev norm of a radial solution remains bounded in its maximal interval of existence, then the solution must exist for all times and scatter.

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