Gevrey class regularity and exponential decay property for Navier-Stokes-\(\alpha\) equations
type: Item
instance of: scholarly article
title: Gevrey class regularity and exponential decay property for Navier-Stokes-\(\alpha\) equations
zbMATH Open document ID: 1185.35179
author: Kaitai Li
author: Yong-Jiang Yu
author: A. X. Huang
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2007-03-20T00:00:00Z
review text: The Navier-Stokes-\(\alpha\) equations were introduced as a closed model of turbulence [see e.g. \textit{C. Foias}, \textit{D. D. Holm} and \textit{E. S. Titi}, Physica D 152--153, 505--519 (2001; Zbl 1037.76022)]. Here the authors study these equations with periodic boundary conditions, and prove analyticity in time for a class of solutions belonging to a Gevrey class. The authors also establish exponential decay of the spatial Fourier spectrum for the analytic solutions, and find the lower bounds for the decay rate. The proof is based on representing the solution as Fourier series, and on introducing some quantities with a clear physical sense (kinetic energy, the instantaneous global rate of dissipation, Kolmogorov length).
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D03
zbMATH DE Number: 5134775
zbMATH Keywords: Gevrey class regularity
zbMATH Keywords: Navier-Stokes-\(\alpha\) equations
zbMATH Keywords: exponential decay
MaRDI profile type: Publication
full work available at URL: s10255-006-0348-x
OpenAlex ID: W2052181532
cites work: Q4040820
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DOI: 10.1007/S10255-006-0348-X
description: scientific article; zbMATH DE number 5134775