Boundary-layer interactions in the plane-parallel incompressible flows

Toan T. Nguyen, Franck Sueur

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

We study the inviscid limit problem of incompressible flows in the presence of both impermeable regular boundaries and a hypersurface transversal to the boundary across which the inviscid flow has a discontinuity jump. In the former case, boundary layers have been introduced by Prandtl as correctors near the boundary between the inviscid and viscous flows. In the latter case, the viscosity smoothes out the discontinuity jump by creating a transition layer which has the same amplitude and thickness as the Prandtl layer. In the neighbourhood of the intersection of the impermeable boundary and of the hypersurface, interactions between the boundary and the transition layers must then be considered. In this paper, we initiate a mathematical study of this interaction and carry out a strong convergence in the inviscid limit for the case of the plane-parallel flows introduced by Di Perna and Majda (1987 Commun. Math. Phys. 108 667-89).

Original languageEnglish (US)
Pages (from-to)3327-3342
Number of pages16
JournalNonlinearity
Volume25
Issue number12
DOIs
StatePublished - Dec 2012

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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