Open Access
2017 Stochastic complex Ginzburg-Landau equation with space-time white noise
Masato Hoshino, Yuzuru Inahama, Nobuaki Naganuma
Electron. J. Probab. 22: 1-68 (2017). DOI: 10.1214/17-EJP125


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.


Download Citation

Masato Hoshino. Yuzuru Inahama. Nobuaki Naganuma. "Stochastic complex Ginzburg-Landau equation with space-time white noise." Electron. J. Probab. 22 1 - 68, 2017.


Received: 20 February 2017; Accepted: 11 November 2017; Published: 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06827081
MathSciNet: MR3742401
Digital Object Identifier: 10.1214/17-EJP125

Primary: 60H15 , 82C28

Keywords: complex Ginzburg-Landau equation , Paracontrolled distribution , regularity structure , renormalization , Stochastic partial differential equation

Vol.22 • 2017
Back to Top