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

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Abstract

We show the global-in-time well-posedness of the complex Ginzburg-Landau (CGL) equation with a space-time white noise on the 3-dimensional torus. Our method is based on Mourrat and Weber (Global well-posedness of the dynamic Φ4 3 model on the torus), where Mourrat and Weber showed the global well-posedness for the dynamical Φ4 3 model. We prove a priori L2p estimate for the paracontrolled solution as in the deterministic case [Phys. D 71 (1994) 285-318].

Original languageEnglish
Pages (from-to)1969-2001
Number of pages33
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume54
Issue number4
DOIs
Publication statusPublished - Nov 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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