Energy critical 2-D stochastic wave equation

We prove the existence and uniqueness of a local maximal solution to a $H^1$-critical stochastic wave equation with multiplicative noise on a smooth bounded domain $\mathcal{D} \subset \mathbb{R}^2$ with exponential nonlinearity. We derive theappropriate deterministic and stochastic Strichartz inequalities in suitable spaces and, then, we show the local well-posedness result for small initial data.