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Viscous profiles of vortex patches

Published online by Cambridge University Press:  08 October 2013

Franck Sueur
Franck Sueur*
Affiliation:
CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France (fsueur@ann.jussieu.fr)
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Abstract

We deal with the incompressible Navier–Stokes equations with vortex patches as initial data. Such data describe an initial configuration for which the vorticity is discontinuous across a hypersurface. We give an asymptotic expansion of the solutions in the vanishing viscosity limit which exhibits an internal layer where the fluid vorticity has a sharp variation. This layer moves with the flow of the Euler equations.

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 14 , Issue 1 , January 2015 , pp. 1 - 68
Copyright
©Cambridge University Press 2013 

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