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

Masato Hoshino, Yuzuru Inahama, Nobuaki Naganuma

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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 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.

Original languageEnglish
Article number104
JournalElectronic Journal of Probability
Volume22
DOIs
Publication statusPublished - Jan 1 2017

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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