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 Carlos E. 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. 

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