For the 3D stochastic wave equation with noise white in time and colored in space, a unique global mild solution exists when drift and diffusion grow at most like |u| (log |u|)^θ, with θ below explicit thresholds.
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Three-dimensional stochastic wave equation with non-Lipschitz coefficients
For the 3D stochastic wave equation with noise white in time and colored in space, a unique global mild solution exists when drift and diffusion grow at most like |u| (log |u|)^θ, with θ below explicit thresholds.