On the Kolmogorov entropy of the weak global attractor of 3D Navier-Stokes equations:Ⅰ

Yong Yang; Bingsheng Zhang

doi:10.3934/dcdsb.2017101

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2017, Volume 22, Issue 6: 2339-2350. Doi: 10.3934/dcdsb.2017101

This issue Previous Article Asymptotic behaviors of Green-Sch potentials at infinity and its applications Next Article Oscillation theorems for impulsive parabolic differential system of neutral type

On the Kolmogorov entropy of the weak global attractor of 3D Navier-Stokes equations:Ⅰ

Yong Yang^1,2, and
Bingsheng Zhang^1,2, ,

1.
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
2.
Department of Mathematics, Texas A & M University, College Station, TX 77843, USA

Author Bio: E-mail address: yyy5104@psu.com
Bingsheng Zhang, E-mail address: shanby.bing@gmail.com
Bingsheng Zhang, E-mail address: shanby.bing@gmail.com

Received: May 31, 2016

Revised: November 30, 2016

Published: May 2017

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Abstract

One particular metric that generates the weak topology on the weak global attractor $\mathcal{A}_w$ of three dimensional incompressible Navier-Stokes equations is introduced and used to obtain an upper bound for the Kolmogorov entropy of $\mathcal{A}_w$. This bound is expressed explicitly in terms of the physical parameters of the fluid flow.

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Mathematics Subject Classification: 35Q30, 76D05, 34G20, 37L05, 37L25.

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