We study the Cauchy problem for the radial energy-critical nonlinear wave equation
in three dimensions. Our main result proves almost-sure scattering for radial initial
data below the energy space. In order to preserve the spherical symmetry of the
initial data, we construct a radial randomization that is based on annular
Fourier multipliers. We then use a refined radial Strichartz estimate to prove
probabilistic Strichartz estimates for the random linear evolution. The main new
ingredient in the analysis of the nonlinear evolution is an interaction flux
estimate between the linear and nonlinear components of the solution. We
then control the energy of the nonlinear component by a triple bootstrap
argument involving the energy, the Morawetz term, and the interaction flux
estimate.
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