On the rate of convergence of the two-dimensional α-models of turbulence to the Navier-Stokes equations

2009/02/24 by Y. Cao, Cao, Y., E. S. Titi +1
Mathematics · Physics and Astronomy · #35A30 #35Q35 #65M12 #65M15 #76D05 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35A30 #msc:35Q35 #msc:65M12 #msc:65M15 #msc:76D05

paper · pdf · doi:10.48550/arxiv.0902.4247

29 pages

arxiv created 2009/10/15 · arxiv updated 2009/12/01

Abstract

Rates of convergence of solutions of various two-dimensional α-regularization models, subject to periodic boundary conditions, toward solutions of the exact Navier-Stokes equations are given in the L^∞-L² time-space norm, in terms of the regularization parameter α, when α approaches zero. Furthermore, as a paradigm, error estimates for the Galerkin approximation of the exact two-dimensional Leray-α model are also presented in the L^∞-L² time-space norm. Simply by the triangle inequality, one can reach the error estimates of the solutions of Galerkin approximation of the α-regularization models toward the exact solutions of the Navier-Stokes equations in the two-dimensional periodic boundary conditions case.

Related

• On the approximation of turbulent fluid flows by the Navier-Stokes-α equations on bounded domains
• Singularity & Regularity Issues for Simplified Models of Turbulence
• On a critical Leray-α model of turbulence
• A high accuracy Leray-deconvolution model of turbulence and its limiting behavior
• On the decay and Gevrey regularity of the solutions to the Navier-Stokes equations in general two-dimensional domains