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 ${\mathcal{H}}^{\mathit{s}}$, $\mathit{s}>\frac{4}{5}$.