Stochastic complex Ginzburg-Landau equation with space-time white noise
Stochastic complex Ginzburg-Landau equation with space-time white noise
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DOI：
10.1214/17-ejp125
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
M. Hoshino;Y. Inahama;Nobuaki Naganuma
中科院分区：
文献类型：
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作者：
M. Hoshino;Y. Inahama;Nobuaki Naganuma
研究了三维环面上具有复值时空白噪声的随机三次复金兹堡-朗道方程。这个非线性方程是如此奇异，以至于它只能在重整化的意义上理解。本文的前半部分在正则结构理论的框架下证明了该方程的局部适定性。后半部分在副控制分布理论的框架下证明了局部适定性。
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 under- stood 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.