JournalsrmiVol. 22, No. 2pp. 489–543

Poches de tourbillon singulières dans un fluide faiblement visqueux

  • Taoufik Hmidi

    Université de Rennes 1, Rennes, France
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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 C1+sC^{1+s} outside a singular set Σ\Sigma, so the velocity is, for all time, lipschitzian outside the image of Σ\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.

Cite this article

Taoufik Hmidi, Poches de tourbillon singulières dans un fluide faiblement visqueux. Rev. Mat. Iberoam. 22 (2006), no. 2, pp. 489–543

DOI 10.4171/RMI/464