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Stochastic complex Ginzburg-Landau equation with space-time white noise. (English) Zbl 1386.60218
Summary: 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.

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
82C28 Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics
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