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

Abstract

AbstractWe 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 $$D^\alpha \xi $$ D α ξ , where $$\alpha < \frac{1}{2}$$ α < 1 2 and $$\xi $$ ξ denotes the space–time white noise.