Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball

Abstract

We establish new results for the radial nonlinear wave and Schrödinger equations on the ball in R2 and R3, for random initial data. More precisely, a well-defined and unique dynamics is obtained on the support of the corresponding Gibbs measure. This complements results from Burq and Tzvetkov (2008) [8,9] and Tzvetkov (2006, 2008) [10,11].