Global well-posedness of complex Ginzburg-Landau equation with a space-time white noise

Abstract

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].

arXiv comment32 pages

References in corpus (2)

• Singular stochastic PDEs
• Stochastic complex Ginzburg-Landau equation with space-time white noise