We show the global-in-time well-posedness of the complex Ginzburg-Landau (CGL) equation with a space-time white noise on the 3-dimensional torus. Our method is based on [14], where Mourrat and Weber showed the global well-posedness for the dynamical $\Phi_3^4$ model. We prove a priori $L^{2p}$ estimate for the paracontrolled solution as in the deterministic case [5].
Three-dimensional Navier-Stokes equations driven by space-time white noise
Modulation Equation for SPDEs in unbounded domains with space-time white noise -- Linear Theory
Paracontrolled quasi-geostrophic equation with space-time white noise
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