Vorticity Measures and the Inviscid Limit

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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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)
Pages (from-to)575-593
Number of pages19
JournalArchive for Rational Mechanics and Analysis
Volume234
Issue number2
DOIs
StatePublished - Nov 1 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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