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On some free boundary problems for the Navier-Stokes equations with moving contact points and lines. (English) Zbl 0926.35116

We study quasistationary free boundary problems for the Navier-Stokes equations governing a viscous flow with moving points of a contact of a free surface with rigid walls of a vessel containing the liquid. A moving contact point can be found in many situations. It plays a central role in such processes as the coating of solid surfaces with a uniform layer of liquid, displacement of one liquid with another one along solid boundaries, spreading of drops on solid surfaces etc. Corresponding free boundary problems are rather difficult for mathematical investigation because of the well-known “problem of the moving contact angle”. The difficulties arise due to the incompatibility of no-slip boundary condition on the rigid wall with boundary conditions on the free surface.

MSC:

35Q30 Navier-Stokes equations
35R35 Free boundary problems for PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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