Translator Disclaimer
November 2018 Global well-posedness of complex Ginzburg–Landau equation with a space–time white noise
Masato Hoshino
Ann. Inst. H. Poincaré Probab. Statist. 54(4): 1969-2001 (November 2018). DOI: 10.1214/17-AIHP862

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 $\Phi_{3}^{4}$ model on the torus), 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 [Phys. D 71 (1994) 285–318].

Nous montrons que l’équation de Ginzburg–Landau complexe (CGL) sur le tore de dimension $3$ avec un bruit blanc en espace-temps est bien posée et admet une solution globale en temps. Notre méthode prend son origine dans Mourrat et Weber (Global well-posedness of the dynamic $\Phi_{3}^{4}$ model on the torus), où Mourrat et Weber montrent ce caractère bien posé global pour le modèle $\Phi^{4}_{3}$ dynamique. Nous établissons une estimée $L^{2p}$ a priori pour la solution paracontrôlée, comme dans le cas déterministe [Phys. D 71 (1994) 285–318].

Citation

Download Citation

Masato Hoshino. "Global well-posedness of complex Ginzburg–Landau equation with a space–time white noise." Ann. Inst. H. Poincaré Probab. Statist. 54 (4) 1969 - 2001, November 2018. https://doi.org/10.1214/17-AIHP862

Information

Received: 24 April 2017; Revised: 18 July 2017; Accepted: 1 September 2017; Published: November 2018
First available in Project Euclid: 18 October 2018

zbMATH: 06996556
MathSciNet: MR3865664
Digital Object Identifier: 10.1214/17-AIHP862

Subjects:
Primary: 60H15, 82C28

Rights: Copyright © 2018 Institut Henri Poincaré

JOURNAL ARTICLE
33 PAGES


SHARE
Vol.54 • No. 4 • November 2018
Back to Top