Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on R³

الأصل · EN

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.