Régularité höldérienne des poches de tourbillon visqueuses

Taoufik Hmidi

doi:10.1016/j.crma.2004.07.027

Régularité höldérienne des poches de tourbillon visqueuses

Translated title of the contribution: Hölderian regularity of the viscous vortex patches

Taoufik Hmidi

Mathematics

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

Abstract

We study the evolution of the Hölderian regularity for some convection-diffusion equation with respect to Lipschitzian vector field, generalizing an earlier result for the Besov spaces B_p,∞^s, with p finite and s ∈ (-1, 1). As an application, we show for the two-dimensional Navier-Stokes system that if the initial vorticity is a vortex patch having a C^1+ε boundary then its image through the viscous flow preserves this regularity for all time with uniform control on the viscosity. We also show some results of inviscid limit.

Translated title of the contribution	Hölderian regularity of the viscous vortex patches
Original language	French
Pages (from-to)	705-708
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	339
Issue number	10
DOIs	https://doi.org/10.1016/j.crma.2004.07.027
State	Published - Nov 15 2004

ASJC Scopus subject areas

General Mathematics

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10.1016/j.crma.2004.07.027

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title = "R{\'e}gularit{\'e} h{\"o}ld{\'e}rienne des poches de tourbillon visqueuses",

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AB - We study the evolution of the Hölderian regularity for some convection-diffusion equation with respect to Lipschitzian vector field, generalizing an earlier result for the Besov spaces Bp,∞s, with p finite and s ∈ (-1, 1). As an application, we show for the two-dimensional Navier-Stokes system that if the initial vorticity is a vortex patch having a C1+ε boundary then its image through the viscous flow preserves this regularity for all time with uniform control on the viscosity. We also show some results of inviscid limit.

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Régularité höldérienne des poches de tourbillon visqueuses

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