The vanishing viscosity limit for some symmetric flows

Gung Min Gie, James P. Kelliher, Milton C. Lopes Filho, Anna L. Mazzucato, Helena J. Nussenzveig Lopes

Research output: Contribution to journalArticle

Abstract

The focus of this paper is on the analysis of the boundary layer and the associated vanishing viscosity limit for two classes of flows with symmetry, namely, Plane-Parallel Channel Flows and Parallel Pipe Flows. We construct explicit boundary layer correctors, which approximate the difference between the Navier–Stokes and the Euler solutions. Using properties of these correctors, we establish convergence of the Navier–Stokes solution to the Euler solution as viscosity vanishes with optimal rates of convergence. In addition, we investigate vorticity production on the boundary in the limit of vanishing viscosity. Our work significantly extends prior work in the literature.

Original languageEnglish (US)
Pages (from-to)1237-1280
Number of pages44
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume36
Issue number5
DOIs
Publication statusPublished - Aug 2019

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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