Stochastic complex Ginzburg-Landau equation with space-time white noise (Probability Symposium)

Abstract

We study the stochastic complex Ginzburg-Landau equation with complex-valued space-time white noise on the three dimensional torus. This nonlinear equation is so singular that it can only be understood in a renormalized sense. We prove local well-posedness of it in the framework of paracontrolled distribution theory. This article is an announcement of the authors full paper with the same title.