Transport-diffusion et viscosité évanescente

Taoufik Hmidi

doi:10.1016/S1631-073X(03)00351-0

Transport-diffusion et viscosité évanescente

Translated title of the contribution: Convection-diffusion and vanishing viscosity

Taoufik Hmidi

Mathematics

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

Abstract

In this paper, we study a convection-diffusion model with respect to a vector field having log-Lipschitz regularity. More precisely, we are interested in the viscous repartition of the mass for the solutions of the corresponding equation. We prove that mass is essentially concentrated around the image, through the flow, of the initial support. This allows us, for non-regular bidimensional vortex patches, to prove the global L^p convergence of the Navier-Stokes vorticity ω_ν to the Eulerian vorticity ω, with p > 1.

Translated title of the contribution	Convection-diffusion and vanishing viscosity
Original language	French
Pages (from-to)	309-312
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	337
Issue number	5
DOIs	https://doi.org/10.1016/S1631-073X(03)00351-0
State	Published - Sep 1 2003

ASJC Scopus subject areas

General Mathematics

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10.1016/S1631-073X(03)00351-0

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abstract = "In this paper, we study a convection-diffusion model with respect to a vector field having log-Lipschitz regularity. More precisely, we are interested in the viscous repartition of the mass for the solutions of the corresponding equation. We prove that mass is essentially concentrated around the image, through the flow, of the initial support. This allows us, for non-regular bidimensional vortex patches, to prove the global Lp convergence of the Navier-Stokes vorticity ων to the Eulerian vorticity ω, with p > 1.",

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AB - In this paper, we study a convection-diffusion model with respect to a vector field having log-Lipschitz regularity. More precisely, we are interested in the viscous repartition of the mass for the solutions of the corresponding equation. We prove that mass is essentially concentrated around the image, through the flow, of the initial support. This allows us, for non-regular bidimensional vortex patches, to prove the global Lp convergence of the Navier-Stokes vorticity ων to the Eulerian vorticity ω, with p > 1.

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Transport-diffusion et viscosité évanescente

Abstract

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