Abstract:
The existence of steady solutions to the problem of the motion of a rigid ball in a cylindrical pipe filled with a viscous incompressible fluid is proved. The cross section of the pipe has an arbitrary form and the fluid flow is governed by the Stokes equations. At the infinity, the velocity profile tends to that of the Poiseuille flow. It is established that a steady solution exists for any position of the ball in the pipe. The ball performs a straight motion along the generatrices of the pipe and its linear and angular velocities depend on the position of the ball's center in the cross section of the cylinder.
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