Global well-posedness of the two-dimensional stochastic viscous nonlinear wave equations

Abstract

We study well-posedness of viscous nonlinear wave equations (vNLW) on the two-dimensional torus with a stochastic forcing. In particular, we prove pathwise global well-posedness of the stochastic defocusing vNLW with an additive stochastic forcing $D^\alpha \xi$, where $\alpha < \frac 12$ and $\xi$ denotes the space-time white noise.