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.