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Archive for Rational Mechanics and Analysis

, Volume 234, Issue 2, pp 575–593 | Cite as

Vorticity Measures and the Inviscid Limit

  • Peter Constantin
  • Milton C. Lopes Filho
  • Helena J. Nussenzveig LopesEmail author
  • Vlad Vicol
Article

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 \(L^1\)-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.

Notes

Acknowledgements

M.C. Lopes Filho acknowledges the support of Conselho Nacional de Desenvolvimento Científico e Tecnológico – CNPq through grant # 306886/2014-6 and of FAPERJ through grant # E-26/202.999/2017 . H.J. Nussenzveig Lopes thanks the support of Conselho Nacional de Desenvolvimento Científico e Tecnológico – CNPq through grant # 307918/2014-9 and of FAPERJ through grant # E-26/202.950/2015. V. Vicol was partially supported by the NSF grant DMS-1652134 and an Alfred P. Sloan Fellowship. P. Constantin was partially supported by the NSF grant DMS-1713985.

The authors thank the referees for their comments, which helped to improve this work.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Instituto de Matematica, Universidade Federal do Rio de JaneiroRio de JaneiroBrazil
  3. 3.Courant Institute, New York UniveristyNew YorkUSA

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