二维纳维-斯托克斯方程的多旋涡和吸引维下限

Pub Date : 2024-06-10 DOI:10.1134/S1064562424702016

A. G. Kostianko, A. A. Ilyin, D. Stone, S. V. Zelik

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引用次数: 0

摘要

本文提出了一种获取纳维-斯托克斯方程吸引子维度下限的新方法，该方法不使用柯尔莫哥洛夫流。通过应用这种方法，可以获得具有 Ekman 阻尼的平面上方程的维数的精确估计值。以前只有在周期性边界条件的情况下才知道类似的估计值。此外，对于二维有界域中的经典纳维-斯托克斯系统，我们也获得了类似的下限，该系统具有迪里夏特边界条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Multi-vortices and Lower Bounds for the Attractor Dimension of 2D Navier–Stokes Equations

A new method for obtaining lower bounds for the dimension of attractors for the Navier–Stokes equations is presented, which does not use Kolmogorov flows. By applying this method, exact estimates of the dimension are obtained for the case of equations on a plane with Ekman damping. Similar estimates were previously known only for the case of periodic boundary conditions. In addition, similar lower bounds are obtained for the classical Navier–Stokes system in a two-dimensional bounded domain with Dirichlet boundary conditions.

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