The Inviscid Limit of Navier–Stokes Equations for Analytic Data on the Half-Space

Toan Nguyen, Trinh T. Nguyen

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In their classical work, Sammartino and Caflisch (Commun Math Phys 192(2):433–461, 1998a; Commun Math Phys 192(2):463–491, 1998b) proved the inviscid limit of the incompressible Navier–Stokes equations for well-prepared data with analytic regularity in the half-space. Their proof is based on the detailed construction of Prandtl’s boundary layer asymptotic expansions. In this paper, we give a direct proof of the inviscid limit for general analytic data without having to construct Prandtl’s boundary layer correctors. Our analysis makes use of the boundary vorticity formulation and the abstract Cauchy–Kovalevskaya theorem on analytic boundary layer function spaces that capture unbounded vorticity.

Original languageEnglish (US)
Pages (from-to)1103-1129
Number of pages27
JournalArchive for Rational Mechanics and Analysis
Volume230
Issue number3
DOIs
StatePublished - Dec 1 2018

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Inviscid Limit
Half-space
Boundary Layer
Navier-Stokes Equations
Boundary layers
Vorticity
Incompressible Navier-Stokes
Corrector
Function Space
Asymptotic Expansion
Regularity
Formulation
Theorem

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

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The Inviscid Limit of Navier–Stokes Equations for Analytic Data on the Half-Space. / Nguyen, Toan; Nguyen, Trinh T.

In: Archive for Rational Mechanics and Analysis, Vol. 230, No. 3, 01.12.2018, p. 1103-1129.

Research output: Contribution to journalArticle

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