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September, 2006 Poches de tourbillon singulières dans un fluide faiblement visqueux
Taoufik Hmidi
Rev. Mat. Iberoamericana 22(2): 489-543 (September, 2006).

Abstract

In this paper, we study the singular vortex patches in the two-dimensional incompressible Navier-Stokes equations. We show, in particular, that if the initial vortex patch is $C^{1+s}$ outside a singular set $\Sigma$, so the velocity is, for all time, lipschitzian outside the image of $\Sigma$ through the viscous flow. In addition, the correponding lipschitzian norm is independant of the viscosity. This allows us to prove some results related to the inviscid limit for the geometric structures of the vortex patch.

Citation

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Taoufik Hmidi . "Poches de tourbillon singulières dans un fluide faiblement visqueux." Rev. Mat. Iberoamericana 22 (2) 489 - 543, September, 2006.

Information

Published: September, 2006
First available in Project Euclid: 26 October 2006

zbMATH: 1127.35037
MathSciNet: MR2294788

Subjects:
Primary: 35A20 , 35Q30 , 76C05

Keywords: Littlewood-Paley theory , Navier-Stokes and Euler equations , vortex patches

Rights: Copyright © 2006 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.22 • No. 2 • September, 2006
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