We study the stochastic cubic 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. In the first half of this paper we prove local well-posedness of this equation in the framework of regularity structure theory. In the latter half we prove local well-posedness in the framework of paracontrolled distribution theory.
"Stochastic complex Ginzburg-Landau equation with space-time white noise." Electron. J. Probab. 22 1 - 68, 2017. https://doi.org/10.1214/17-EJP125