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

TL;DR

This paper proves the global well-posedness of a two-dimensional stochastic viscous nonlinear wave equation with additive white noise, advancing understanding of stochastic PDEs with nonlinear and viscous effects.

Contribution

It establishes the pathwise global well-posedness of the stochastic defocusing viscous nonlinear wave equation with additive noise on a 2D torus, a novel result in stochastic PDE theory.

Findings

Proves global well-posedness for stochastic vNLW with additive noise.

Handles noise with regularity less than 1/2, specifically $D^ extalpha \xi$ with extalpha<1/2.

Provides a rigorous mathematical framework for 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.