M. Bildhauer, M. Fuchs
On the exterior problem in 2D for stationary flows of fluids with shear dependent viscosity

Comment.Math.Univ.Carolin. 53,2 (2012) 221-236.

Abstract: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.

Keywords: equations of Navier-Stokes type, stationary case, exterior problem in~2D
AMS Subject Classification: 76D05 35Q30