含时空白噪声的随机复Ginzburg-Landau方程
Stochastic complex Ginzburg-Landau equation with space-time white noise
摘要：
研究了三维环面上带复值时空白噪声的随机三次复Ginzburg-Landau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被理解。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。在后半部分，我们证明了局部适定性的框架下的仿控制分布理论。
英文摘要：
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 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.
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