Remarks on the inviscid limit for the Navier-Stokes equations for uniformly bounded velocity fields

Peter Constantin, Tarek Elgindi, Mihaela Ignatova, Vlad Vicol

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the vanishing viscosity limit of the Navier-Stokes equations in a half-plane, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at x2 = 0. A sufficient condition for this to hold is that the tangential Navier-Stokes velocity remains uniformly bounded and has a uniformly integrable tangential gradient near the boundary.

Original languageEnglish (US)
Pages (from-to)1932-1946
Number of pages15
JournalSIAM Journal on Mathematical Analysis
Volume49
Issue number3
DOIs
StatePublished - 2017

Keywords

  • Euler equations
  • Inviscid limit
  • Navier-Stokes equations

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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