Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on [formula omitted

Abstract

We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on R3 with random initial data in Hs(R3)×Hs−1(R3) for s>12. The main new ingredient is a uniform probabilistic energy bound for approximating random solutions.