Stochastic complex Ginzburg-Landau equation with space-time white noise

Abstract

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 under- stood 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.

arXiv commentTypos was fixed

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