Abstract

The two-dimensional system of Navier–Stokes equations in a medium with anisotropic variable viscosity and periodic small obstacles is considered. It is proved that the trajectory attractors of the system tend in a certain weak topology to the trajectory attractors of the homogenized system of Navier–Stokes equations with an additional potential in a medium without obstacles.

中文翻译：

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具有小周期性障碍的各向异性介质中纳维-斯托克斯系统吸引子的渐近性

摘要

考虑具有各向异性变粘度和周期性小障碍物的二维纳维-斯托克斯方程组。证明了在无障碍介质中，系统的轨迹吸引子趋于某种弱拓扑，趋于具有附加势的均质Navier-Stokes方程组的轨迹吸引子。