Vorticity Measures and the Inviscid Limit

Peter Constantin, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes, Vlad Vicol

Research output: Contribution to journalArticle

Abstract

We consider a sequence of Leray-Hopf weak solutions of the 2D Navier-Stokes equations on a bounded domain, in the vanishing viscosity limit. We provide sufficient conditions on the associated vorticity measures, away from the boundary, which ensure that as the viscosity vanishes the sequence converges to a weak solution of the Euler equations. The main assumptions are local interior uniform bounds on the L1-norm of vorticity and the local uniform convergence to zero of the total variation of vorticity measure on balls, in the limit of vanishing ball radii.

Original languageEnglish (US)
JournalArchive for Rational Mechanics and Analysis
DOIs
StatePublished - Jan 1 2019

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Inviscid Limit
Vorticity
Weak Solution
Ball
Viscosity
Vanishing Viscosity
Uniform Bound
L1-norm
Euler equations
Local Convergence
Total Variation
Uniform convergence
Euler Equations
Navier Stokes equations
Bounded Domain
Vanish
Navier-Stokes Equations
Interior
Radius
Converge

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

Constantin, P., Lopes Filho, M. C., Nussenzveig Lopes, H. J., & Vicol, V. (2019). Vorticity Measures and the Inviscid Limit. Archive for Rational Mechanics and Analysis. https://doi.org/10.1007/s00205-019-01398-1

Vorticity Measures and the Inviscid Limit. / Constantin, Peter; Lopes Filho, Milton C.; Nussenzveig Lopes, Helena J.; Vicol, Vlad.

In: Archive for Rational Mechanics and Analysis, 01.01.2019.

Research output: Contribution to journalArticle

Constantin, Peter ; Lopes Filho, Milton C. ; Nussenzveig Lopes, Helena J. ; Vicol, Vlad. / Vorticity Measures and the Inviscid Limit. In: Archive for Rational Mechanics and Analysis. 2019.
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