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On the Oseen vortices in dimension N = 2 for the inhomogeneous Navier-Stokes equations for radial initial density

Haspot, Boris (2016), On the Oseen vortices in dimension N = 2 for the inhomogeneous Navier-Stokes equations for radial initial density. https://basepub.dauphine.fr/handle/123456789/17176

Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01419561
Date
2016
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
14
Metadata
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Author(s)
Haspot, Boris
Abstract (EN)
This paper is dedicated to the proof of the existence of Lamb Oseen vortex for the inhomogeneous Navier-Stokes equation when N = 2. We restrict our study to the case of radial initial data ρ 0 which belongs to C α (R 2) with 0 < α < 1. To do this we recall the construction of fundamental solution for reaction diffusion equations. We point out that when ρ 0 = 1, our Lamb Oseen solution are not self similar. We prove also that the vorticity of inhomogeneous Navier-Stokes equations (when curlu 0 is radial and in L 1 (R 2)) converges asymptotically in time to the Oseen solution of Navier Stokes equation provided that the fluctuation of the initial density is sufficiently small.
Subjects / Keywords
Lamb Oseen vortex; Navier-Stokes equation

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