Stochastic wave equation with critical nonlinearities: Temporal regularity and uniqueness

AbstractWe consider a nonlinear wave equation utt=Δu+f(u)+g(u)W˙ on Rd driven by a spatially homogeneous Wiener process W with a finite spectral measure and with nonlinear terms f, g of critical growth. We study pathwise uniqueness and norm continuity of paths of (u,ut) in H1(Rd)⊕L2(Rd) under the hypothesis that there exists a local solution u such that (u,ut) has weakly continuous paths in H1(Rd)⊕L2(Rd)