Energy critical 2-D stochastic wave equations

Abstract

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