时空白噪声驱动下三维Navier-斯托克斯方程的近似解
Approximating three-dimensional Navier-Stokes equations driven by space-time white noise
摘要：
本文研究了时空白噪声驱动的三维Navier-Stokes（NS）方程的仿控制分布近似。最近在[ZZ 14]中，基于正则结构理论和仿控制分布，发展了这类方程的解理论。为了使近似方程收敛到时空白噪声驱动的三维NS方程，需要在近似方程中减去漂移项。这些漂移项来自于解理论中的重正化，收敛于解乘以取决于近似的某个常数。
英文摘要：
In this paper we study approximations to 3D Navier-Stokes (NS) equation driven by space-time white noise by paracontrolled distribution proposed in [GIP13]. A solution theory for this equation has been developed recently in [ZZ14] based on regularity structure theory and paracontrolled distribution. In order to make the approximating equation converge to 3D NS equation driven by space-time white noise, we should subtract some drift terms in approximating equations. These drift terms, which come from renormalizations in the solution theory, converge to the solution multiplied by some constant depending on approximations.
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