Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ${\mathbb{R}}^3$

Abstract

We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ${\mathbb{R}}^3$ with random initial data in $H^s({\mathbb{R}}^3)\times H^{s-1}({\mathbb{R}}^3)$ for $s>\frac{1}{2}$. The main new ingredient is a uniform probabilistic energy bound for approximating random solutions.

26 pages. Expanded the introduction. To appear in J. Math. Pures Appl

References in corpus (2)

• Ill-posedness for nonlinear Schrodinger and wave equations
• On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on ${\mathbb{R}}^d$, $d\ge 3$

Cited by in corpus (2)

• On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on ${\mathbb{R}}^d$, $d\ge 3$
• On the almost sure global well-posedness of energy sub-critical nonlinear wave equations on ${\mathbb{R}}^3$