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Publication 14-CNA-028
Gung-Min Gie Christopher Henderson Gautam Iyer Landon Kavlie Jared P. Whitehead Abstract: We study the long-time behavior an extended Navier-Stokes system
in $\mathbb{R^2}$ where the incompressibility constraint is relaxed.
This is one of
several "reduced models" of Grubb and Solonnikov '89 and was revisited
recently (Liu, Liu, Pego '07) in bounded domains in order to explain
the fast convergence of certain numerical schemes (Johnston, Liu '04).
Our first result shows that if the initial divergence of the fluid velocity
is mean zero, then the Oseen vortex is globally asymptotically stable.
This is the same as the Gallay Wayne '05 result for the standard Navier-
Stokes equations. When the initial divergence is not mean zero, we show
that the analogue of the Oseen vortex exists and is stable under small
perturbations. For completeness, we also prove global well-posedness of
the system we study.Get the paper in its entirety as 14-CNA-028.pdf |