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On the exterior problem in 2D for stationary flows of fluids with shear dependent viscosity

Michael BildhauerMartin Fuchs — 2012

Commentationes Mathematicae Universitatis Carolinae

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 | B = 0 and lim | x | | x | 1 / 3 | u ( x ) | = 0 uniformly. For slow flows the latter condition can be replaced by lim | x | | u ( x ) | = 0 uniformly. In particular, these results hold for the classical Navier-Stokes case.

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