Vorticity internal transition layers for the Navier-Stokes equations

Franck Sueur[1]

  • [1] Laboratoire Jacques-Louis Lions Université Pierre et Marie Curie - Paris 6; 175 Rue du Chevaleret 75013 Paris, FRANCE

Journées Équations aux dérivées partielles (2008)

  • page 1-15
  • ISSN: 0752-0360

Abstract

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We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show -thanks to an asymptotic expansion- that there is a sharp but smooth variation of the fluid vorticity into a internal layer moving with the flow of the Euler equations; as long as this later exists and as t < < 1 / ν , where ν is the viscosity coefficient.

How to cite

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Sueur, Franck. "Vorticity internal transition layers for the Navier-Stokes equations." Journées Équations aux dérivées partielles (2008): 1-15. <http://eudml.org/doc/10640>.

@article{Sueur2008,
abstract = {We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show -thanks to an asymptotic expansion- that there is a sharp but smooth variation of the fluid vorticity into a internal layer moving with the flow of the Euler equations; as long as this later exists and as $ t &lt;&lt; 1/\nu $, where $\nu $ is the viscosity coefficient.},
affiliation = {Laboratoire Jacques-Louis Lions Université Pierre et Marie Curie - Paris 6; 175 Rue du Chevaleret 75013 Paris, FRANCE},
author = {Sueur, Franck},
journal = {Journées Équations aux dérivées partielles},
language = {eng},
month = {6},
pages = {1-15},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Vorticity internal transition layers for the Navier-Stokes equations},
url = {http://eudml.org/doc/10640},
year = {2008},
}

TY - JOUR
AU - Sueur, Franck
TI - Vorticity internal transition layers for the Navier-Stokes equations
JO - Journées Équations aux dérivées partielles
DA - 2008/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 15
AB - We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show -thanks to an asymptotic expansion- that there is a sharp but smooth variation of the fluid vorticity into a internal layer moving with the flow of the Euler equations; as long as this later exists and as $ t &lt;&lt; 1/\nu $, where $\nu $ is the viscosity coefficient.
LA - eng
UR - http://eudml.org/doc/10640
ER -

References

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