Global well-posedness of the two-dimensional stochastic nonlinear wave equation on an unbounded domain

Abstract

We study the two-dimensional wave equation with cubic nonlinearity posed on ${\mathbb{R}}^2$, with space-time white noise forcing. After a suitable renormalisation of the nonlinearity, we prove global well-posedness for this equation for initial data in ${\mathcal{H}}^s$, $s>\frac{4}{5}$.

23 pages, 0 figures

References in corpus (2)

• Random data Cauchy theory for supercritical wave equations I: Local theory
• Random data Cauchy theory for supercritical wave equations II : A global existence result

Cited by in corpus (3)

• Three-dimensional stochastic cubic nonlinear wave equation with almost space-time white noise
• Norm inflation for a non-linear heat equation with Gaussian initial conditions
• Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus