Sublayer of Prandtl Boundary Layers

Emmanuel Grenier, Toan T. Nguyen

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

The aim of this paper is to investigate the stability of Prandtl boundary layers in the vanishing viscosity limit ν→ 0. In Grenier (Commun Pure Appl Math 53(9):1067–1091, 2000), one of the authors proved that there exists no asymptotic expansion involving one of Prandtl’s boundary layer, with thickness of order ν, which describes the inviscid limit of Navier–Stokes equations. The instability gives rise to a viscous boundary sublayer whose thickness is of order ν3 / 4. In this paper, we point out how the stability of the classical Prandtl’s layer is linked to the stability of this sublayer. In particular, we prove that the two layers cannot both be nonlinearly stable in L. That is, either the Prandtl’s layer or the boundary sublayer is nonlinearly unstable in the sup norm.

Original languageEnglish (US)
Pages (from-to)1139-1151
Number of pages13
JournalArchive for Rational Mechanics and Analysis
Volume229
Issue number3
DOIs
StatePublished - Sep 1 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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