Asymptotic stability of Oseen vortices for a density dependent incompressible viscous fluid

Asymptotic stability of Oseen vortices for a density-dependent incompressible viscous fluid L.Miguel Rodrigues Institut Fourier Universite Grenoble 1, C.N.R.S. 100 rue des maths 38402 Saint-Martin-d'Heres, France Abstract In the analysis of the long-time behavior of two-dimensional incompressible viscous fluids, Oseen vortices play a major role as attractors of any homoge- neous solution with integrable initial vorticity [8]. As a first step in the study of the density-dependent case, the present paper establishes the asymptotic stabil- ity of Oseen vortices for slightly inhomogeneous fluids with respect to localized perturbations. Resume Les tourbillons d'Oseen occupent une place majeure dans la description du comportement asymptotique en temps des fluides bidimensionnelles incompress- ibles et visqueux, en tant qu'attracteurs de toute solution homogene de vorticite initiale integrable [8]. Premiere etape dans l'analyse du cas inhomogene, cet ar- ticle etablit la stabilite asymptotique des tourbillons d'Oseen, vis-a-vis de per- turbations localisees, en tant que fluides a densite variable. Mathematics subject classification (2000). 76D05, 35Q30, 35B35. Keywords. Density-dependent incompressible Navier-Stokes equations, weak inhomogeneity, Oseen vortex, asymptotic stability, self-similar variables, vortic- ity equation.

• lp-space defined


• density-dependent model


• w˜ ?


• oseen vortices


• stabilite asymptotique des tourbillons d'oseen


• hilbert space


• navier stokes equations


• dependent incompressible


• incompressible navier-stokes equations