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

被引：10

作者：

Hoshino, Masato ^{[1
]}

Inahama, Yuzuru ^{[2
]}

Naganuma, Nobuaki ^{[3
]}

机构：

[1] Waseda Univ, Sch Fundamental Sci & Engn, Shinjuku Ku, Tokyo 1698555, Japan

[2] Kyushu Univ, Grad Sch Math, Nishi Ku, Fukuoka 8190395, Japan

[3] Osaka Univ, Grad Sch Engn Sci, Toyonaka, Osaka 5608531, Japan

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2017年 / 22卷

关键词：

stochastic partial differential equation; complex Ginzburg-Landau equation; regularity structure; paracontrolled distribution; renormalization; KPZ EQUATION; ERGODICITY;

D O I：

10.1214/17-EJP125

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页数：68

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