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

Masato Hoshino; Yuzuru Inahama; Nobuaki Naganuma

doi:10.1214/17-EJP125

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

Masato Hoshino, Yuzuru Inahama, Nobuaki Naganuma

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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.

Original language	English
Article number	104
Journal	Electronic Journal of Probability
Volume	22
DOIs	https://doi.org/10.1214/17-EJP125
Publication status	Published - 2017

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/17-EJP125

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title = "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.",

author = "Masato Hoshino and Yuzuru Inahama and Nobuaki Naganuma",

note = "Funding Information: The authors thank Professor Reika Fukuizumi of Tohoku University for stimulating discussions and valuable advice. They also thank Professor Makoto Katori of Chuo University for helpful comments. The first named author was partially supported by JSPS KAKENHI Grant Number JP16J03010. The second named author was partially supported by JSPS KAKENHI Grant Number JP15K04922. The third named author was partially supported by JSPS KAKENHI Grant Number JP17K14202. Publisher Copyright: {\textcopyright} 2017, University of Washington. All rights reserved.",

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doi = "10.1214/17-EJP125",

language = "English",

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journal = "Electronic Journal of Probability",

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T1 - Stochastic complex Ginzburg-Landau equation with space-time white noise

AU - Hoshino, Masato

AU - Inahama, Yuzuru

AU - Naganuma, Nobuaki

N1 - Funding Information: The authors thank Professor Reika Fukuizumi of Tohoku University for stimulating discussions and valuable advice. They also thank Professor Makoto Katori of Chuo University for helpful comments. The first named author was partially supported by JSPS KAKENHI Grant Number JP16J03010. The second named author was partially supported by JSPS KAKENHI Grant Number JP15K04922. The third named author was partially supported by JSPS KAKENHI Grant Number JP17K14202. Publisher Copyright: © 2017, University of Washington. All rights reserved.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

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JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

M1 - 104

ER -

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

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