Abstract

We consider incompressible Navier–Stokes equations in a bounded 2D domain, complete with the so-called dynamic slip boundary conditions. Assuming that the data are regular, we show that weak solutions are strong. As an application, we provide an explicit upper bound of the fractal dimension of the global attractor in terms of the physical parameters. These estimates comply with analogous results in the case of Dirichlet boundary condition.

中文翻译：

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具有动态边界条件的二维 NSE 的强解和吸引子维数

摘要

我们考虑有界二维域中的不可压缩纳维-斯托克斯方程，并具有所谓的动态滑移边界条件。假设数据是规则的，我们表明弱解也是强解。作为一个应用，我们根据物理参数提供了全局吸引子分形维数的显式上限。这些估计符合狄利克雷边界条件情况下的类似结果。