Plane capillary flow of a viscous fluid with multiply connected boundary in the Stokes approximation (Q1317664)

The plane capillary flow of a viscous incompressible fluid in a region with multiply connected cylindrical boundary of arbitrary shape is studied under Stokes approximation. In the course of relaxation, the internal cavities collapse, and the cylinder acquires a circular configuration asymptotically. It is shown that the true pressure distribution gives a minimum of the integral of the square of the pressure over the region for fixed integral of the pressure over the boundary. The pressure and the velocity field on the boundary are calculated. Upper bounds for the law of decrease of the perimeter of the region and for the time during which the number of connected components of the boundary remains unchanged, are obtained.