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In this paper, we consider the wave equation in space dimension 3 with anenergy-supercritical, focusing nonlinearity. We show that any radial solutionof the equation which is bounded in the critical Sobolev space is globallydefined and scatters to a linear solution. As a consequence, finite timeblow-up solutions have critical Sobolev norm converging to infinity (along somesequence of times). The proof relies on the compactness/rigidity method,pointwise estimates on compact solutions obtained by the two last authors, andchannels of energy arguments used by the authors in previous works on theenergy-critical equation.

Scattering for radial, bounded solutions of focusing supercritical wave equations