Asymptotic analysis of the linearized Navier-Stokes equation on an exterior circular domain: Explicit solution and the zero viscosity limit

Maria Carmela Lombardo, Russel Caflisch, Marco Sammartino

Research output: Contribution to journalArticle

Abstract

In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity.

Original languageEnglish (US)
Pages (from-to)335-354
Number of pages20
JournalCommunications in Partial Differential Equations
Volume26
Issue number1-2
StatePublished - 2001

Fingerprint

Asymptotic analysis
Corrector
Explicit Solution
Square root
Asymptotic Analysis
Sobolev Spaces
Navier Stokes equations
Boundary Layer
Explicit Formula
Viscosity
Two Dimensions
Navier-Stokes Equations
Norm
Zero
Term
Sobolev spaces
Boundary layers

Keywords

  • Asymptotic analysis
  • Boundary layer
  • Explicit solutions
  • Navier-Stokes equations
  • Stokes equations
  • Zero viscosity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Asymptotic analysis of the linearized Navier-Stokes equation on an exterior circular domain : Explicit solution and the zero viscosity limit. / Lombardo, Maria Carmela; Caflisch, Russel; Sammartino, Marco.

In: Communications in Partial Differential Equations, Vol. 26, No. 1-2, 2001, p. 335-354.

Research output: Contribution to journalArticle

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