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 $\alpha <\frac{1}{2}$ and $\xi$ denotes the space-time white noise.

arXiv comment28 pages. The case of randomized initial data is moved to Remark 1.4 (iii). To appear in Stoch. Partial Differ. Equ. Anal. Comput