On the almost sure global well-posedness of energy sub-critical nonlinear wave equations on ${\mathbb{R}}^3$

Abstract

We consider energy sub-critical defocusing nonlinear wave equations on ${\mathbb{R}}^3$ and establish the existence of unique global solutions almost surely with respect to a unit-scale randomization of the initial data on Euclidean space. In particular, we provide examples of initial data at super-critical regularities which lead to unique global solutions. The proof is based on probabilistic growth estimates for a new modified energy functional. This work improves upon the authors' previous results in [25] by significantly lowering the regularity threshold and strengthening the notion of uniqueness.

arXiv comment15 pages, 1 figure, minor typos corrected and references updated

References in corpus (4)

• Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L^2(T)
• Ill-posedness for nonlinear Schrodinger and wave equations
• Solutions globales pour l'équation de Schrödinger cubique en dimension 3
• Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ${\mathbb{R}}^3$

Cited by in corpus (2)

• Almost sure scattering for the radial energy critical nonlinear wave equation in three dimensions
• Almost Sure Existence of Global Solutions for Supercritical Semilinear Wave Equations