Local solution to an energy critical 2-D stochastic wave equation with exponential nonlinearity in a bounded domain

We prove the existence and uniqueness of a local maximal solution to an H1-critical stochastic wave equation with multiplicative noise on smooth bounded domain D⊂R2 exponential nonlinearity. First, we derive appropriate deterministic Strichartz inequalities in suitable spaces and, then use them arguments based fixed point method show well-posedness result. also present explosion result for constructed unique solution.