Uniqueness for stochastic non-linear wave equations (Q2382616)

The author consider a wave equation in \(\mathbb{R}^d\) of the type \[ \partial_t^2 u =\Delta u +f(u)+g(u) \dot{W}\;. \] with locally Lipschitz non-linearities \(g\) and \(f\) of subcritical growth. The noise \( \dot{W}\) is Gaussian, white in time, and spatially homogeneous. The main results prove uniqueness of weak solutions as stochastic processes in \(H^1\). Improving previously known stochastic results, the author closes the gap between critical growth of nonlinearities in the deterministic and the stochastic case in dimension \(d\geq3\).