## Electronic Journal of Probability

### Stochastic complex Ginzburg-Landau equation with space-time white noise

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 104, 68 pp.

Dates
Accepted: 11 November 2017
First available in Project Euclid: 15 December 2017

https://projecteuclid.org/euclid.ejp/1513349792

Digital Object Identifier
doi:10.1214/17-EJP125

Mathematical Reviews number (MathSciNet)
MR3742401

Zentralblatt MATH identifier
06827081

#### Citation

Hoshino, Masato; Inahama, Yuzuru; Naganuma, Nobuaki. Stochastic complex Ginzburg-Landau equation with space-time white noise. Electron. J. Probab. 22 (2017), paper no. 104, 68 pp. doi:10.1214/17-EJP125. https://projecteuclid.org/euclid.ejp/1513349792

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