Global well-posedness of complex Ginzburg-Landau equation with a space-time white noise
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 [14], where Mourrat and Weber showed the global well-posedness for the dynamical $\Phi_3^4$ model. We prove a priori $L^{2p}$ estimate for the paracontrolled solution as in the deterministic case [5].
- Publication:
-
Annales de L'Institut Henri Poincare Section (B) Probability and Statistics
- Pub Date:
- November 2018
- DOI:
- 10.1214/17-AIHP862
- arXiv:
- arXiv:1704.04396
- Bibcode:
- 2018AIHPB..54.1969H
- Keywords:
-
- Mathematics - Probability;
- 60H15;
- 82C28
- E-Print:
- 32 pages