A geometric analysis of the Lagerstrom model problem

N Popovic*, P Smolyan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Lagerstrom's model problem is a classical singular perturbation problem which was introduced to illustrate the ideas and subtleties involved in the analysis of viscous flow past a solid at low Reynolds number by the method of matched asymptotic expansions. In this paper the corresponding boundary value problem is analyzed geometrically by using methods from the theory of dynamical systems, in particular invariant manifold theory. As an essential part of the dynamics takes place near a line of non-hyperbolic equilibria, a blow-up transformation is introduced to resolve these singularities. This approach leads to a constructive proof of existence and local uniqueness of solutions and to a better understanding of the singular perturbation nature of the problem. In particular, the source of the logarithmic switchback phenomenon is identified. (C) 2003 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)290-325
Number of pages36
JournalJournal of Differential Equations
Volume199
Issue number2
DOIs
Publication statusPublished - 20 May 2004

Keywords / Materials (for Non-textual outputs)

  • singular perturbations
  • invariant manifolds
  • blow-up
  • LOW-REYNOLDS-NUMBER
  • SINGULAR PERTURBATION-THEORY
  • CIRCULAR CYLINDER
  • VISCOUS-FLOW
  • EXPANSIONS
  • EQUATION
  • POINTS

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