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Zbl 1159.76014
Rodrigues, L.Miguel
Asymptotic stability of Oseen vortices for a density-dependent incompressible viscous fluid. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 2, 625-648 (2009). ISSN 0294-1449

Summary: In the analysis of the long-time behavior of two-dimensional incompressible viscous fluids, Oseen vortices play a major role as attractors of any homogeneous solution with integrable initial vorticity [{\it T. Gallay} and {\it C. E. Wayne}, Commun. Math. Phys. 255, No.~1, 97--129 (2005; Zbl 1139.35084 )]. As a first step in the study of the density-dependent case, the present paper establishes the asymptotic stability of Oseen vortices for slightly inhomogeneous fluids with respect to localized perturbations.

MSC 2000:: *76E99 Hydrodynamic stability
76D07 Stokes flows
35Q30 Stokes and Navier-Stokes equations
35B35 Stability of solutions of PDE

Keywords: Navier-Stokes equations; weak inhomogeneity; self-similar variables; localized perturbations

Citations: Zbl 1139.35084

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