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].
|Number of pages||33|
|Journal||Annales de l'institut Henri Poincare (B) Probability and Statistics|
|Publication status||Published - Nov 2018|
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty