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

@article{Kenig2008NondispersiveRS, title={Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications}, author={Carlos E. Kenig and Frank Merle}, journal={American Journal of Mathematics}, year={2008}, volume={133}, pages={1029 - 1065} }

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.

## 125 Citations

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for a large class of radially…

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