Boundary regularity of flows under perfect slip boundary conditions

Petr Kaplický; Jakub Tichý

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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.

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