Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations
Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations
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DOI：
10.1017/prm.2018.33
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发表时间：
2019-04-01
影响因子：
1.3
通讯作者：
Dai, Mimi
中科院分区：
文献类型：
--
作者：
Cheskidov, Alexey;Dai, Mimi
科尔莫戈罗夫的湍流理论预测，只有低于某个临界值的波数才是描述三维(3D)流体流动的关键。确定波数是由FOIAs和Prodi首先为二维Navier-Stokes方程引入的，它是Kolmogorov数的数学模拟。本文的目的是证明三维Navier-Stokes方程的时间平均有界于Kolmogorov耗散波数的三维Navier-Stokes方程对其全局吸引子上所有间歇性不是极端的解存在依赖于时间的确定波数。
Kolmogorov's theory of turbulence predicts that only wavenumbers below some critical value, called Kolmogorov's dissipation number, are essential to describe the evolution of a three-dimensional (3D) fluid flow. A determining wavenumber, first introduced by Foias and Prodi for the 2D Navier-Stokes equations, is a mathematical analogue of Kolmogorov's number. The purpose of this paper is to prove the existence of a time-dependent determining wavenumber for the 3D Navier-Stokes equations whose time average is bounded by Kolmogorov's dissipation wavenumber for all solutions on the global attractor whose intermittency is not extreme.