Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of Vortex Solutions to an Extended Navier-Stokes System   We study the long-time behavior an extended Navier-Stokes system in $\R^2$
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.

15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con