Stochastic wave equation with critical nonlinearities: temporal regularity and uniqueness
The nonlinear, \(\mathbb R^d\)-valued wave equation \(u_{tt}=\triangle u+f(u)+g(u)\dot W\) is considered, where \(W\) is a spatially homogeneous Wiener process with finite spectral measure. The functions \(f,g\) are nonlinear and of critical growth. Consider a local solution \(u\). The author studies pathwise uniqueness and norm continuity for \((u,u_t)\) in \(H^1\oplus L^2\).
scientific article; zbMATH DE number 5687474
scientific article