Geodesic
On the exterior problem in 2D for stationary flows of fluids with shear dependent viscosity
Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 2, pp. 221-236

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On the complement of the unit disk $B$ we consider solutions of the equations describing the stationary flow of an incompressible fluid with shear dependent viscosity. We show that the velocity field $u$ is equal to zero provided $u|_{\partial B} = 0$ and $\lim_{|x| \to \infty} |x|^{1/3} |u (x)| = 0$ uniformly. For slow flows the latter condition can be replaced by $\lim_{|x| \to \infty} |u (x)| = 0$ uniformly. In particular, these results hold for the classical Navier-Stokes case.
Classification : 35Q30, 76D05
Keywords: equations of Navier-Stokes type; stationary case; exterior problem in 2D 
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     author = {Bildhauer, M. and Fuchs, M.},
     title = {On the exterior problem in {2D} for stationary flows of fluids with shear dependent viscosity},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {221--236},
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     zbl = {1265.35257},
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Bildhauer, M.; Fuchs, M. On the exterior problem in 2D for stationary flows of fluids with shear dependent viscosity. Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 2, pp. 221-236. http://geodesic.mathdoc.fr/item/CMUC_2012__53_2_a4/