Poches de tourbillon singulières dans un fluide faiblement visqueux

Taoufik Hmidi

doi:10.4171/RMI/464

Poches de tourbillon singulières dans un fluide faiblement visqueux

Taoufik Hmidi

Mathematics

Research output: Contribution to journal › Article › peer-review

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 ∑, so the velocity is, for all time, lipschitzian outside the image of ∑ 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.

Original language	Spanish
Pages (from-to)	489-543
Number of pages	55
Journal	Revista Matematica Iberoamericana
Volume	22
Issue number	2
DOIs	https://doi.org/10.4171/RMI/464
State	Published - 2006

Keywords

Inviscid limit
Littlewood-Paley theory
Navier-Stokes and Euler equations
Singular vortex patches

ASJC Scopus subject areas

General Mathematics

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10.4171/RMI/464

Cite this

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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+s outside a singular set ∑, so the velocity is, for all time, lipschitzian outside the image of ∑ 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 = "Inviscid limit, Littlewood-Paley theory, Navier-Stokes and Euler equations, Singular vortex patches",

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AB - 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+s outside a singular set ∑, so the velocity is, for all time, lipschitzian outside the image of ∑ 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.

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KW - Littlewood-Paley theory

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KW - Singular vortex patches

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Poches de tourbillon singulières dans un fluide faiblement visqueux

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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