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Pré-Publication, Document De Travail Année : 2016

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

Résumé

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.
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Dates et versions

hal-01419561 , version 1 (19-12-2016)

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  • HAL Id : hal-01419561 , version 1

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Boris Haspot. On the Oseen vortices in dimension N = 2 for the inhomogeneous Navier-Stokes equations for radial initial density. 2016. ⟨hal-01419561⟩
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