VANISHING VISCOSITY PLANE PARALLEL CHANNEL FLOW AND RELATED SINGULAR PERTURBATION PROBLEMS

Anna Mazzucato, Michael Taylor

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

Abstract

We study a special class of solutions to the three-dimensional Navier–Stokes equations (Formula Presented), with no-slip boundary condition, on a domain of the form (Formula Presented), dealing with velocity fields of the form (Formula Presented), describing plane-parallel channel flows. We establish results on convergence (Formula Presented), 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.

Original languageEnglish (US)
Pages (from-to)35-93
Number of pages59
JournalAnalysis and PDE
Volume1
Issue number1
DOIs
StatePublished - 2008

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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