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2008 Vanishing viscosity plane parallel channel flow and related singular perturbation problems
Anna Mazzucato, Michael Taylor
Anal. PDE 1(1): 35-93 (2008). DOI: 10.2140/apde.2008.1.35

Abstract

We study a special class of solutions to the three-dimensional Navier–Stokes equations tuν+uνuν+pν=νΔuν, with no-slip boundary condition, on a domain of the form Ω={(x,y,z):0z1}, dealing with velocity fields of the form uν(t,x,y,z)=(vν(t,z),wν(t,x,z),0), describing plane-parallel channel flows. We establish results on convergence uνu0 as ν0, where u0 solves the associated Euler equations. These results go well beyond previously established L2-norm convergence, and provide a much more detailed picture of the nature of this convergence. Carrying out this analysis also leads naturally to consideration of related singular perturbation problems on bounded domains.

Citation

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Anna Mazzucato. Michael Taylor. "Vanishing viscosity plane parallel channel flow and related singular perturbation problems." Anal. PDE 1 (1) 35 - 93, 2008. https://doi.org/10.2140/apde.2008.1.35

Information

Received: 17 December 2007; Revised: 19 March 2008; Accepted: 30 May 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1160.35329
MathSciNet: MR2431354
Digital Object Identifier: 10.2140/apde.2008.1.35

Subjects:
Primary: 35B25 , 35K20 , 35Q30

Keywords: boundary layer , Navier–Stokes equations , Singular perturbation , viscosity

Rights: Copyright © 2008 Mathematical Sciences Publishers

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