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Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 133, Number 4, August 2011
- pp. 1029-1065
- 10.1353/ajm.2011.0029
- Article
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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.