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

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