Revista Matemática Iberoamericana

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Volume 22, Issue 2, 2006, pp. 489–543
DOI: 10.4171/RMI/464

Published online: 2006-08-31

Poches de tourbillon singulières dans un fluide faiblement visqueux

Taoufik Hmidi[1]

(1) Université de Rennes 1, Rennes, France

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.

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

Hmidi Taoufik: Poches de tourbillon singulières dans un fluide faiblement visqueux. Rev. Mat. Iberoam. 22 (2006), 489-543. doi: 10.4171/RMI/464