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The solvability of a free boundary problem for the stationary Navier-Stokes equations with a dynamic contact line. (English) Zbl 0853.35134

We consider the plane steady-state problem with two free boundaries for the Navier-Stokes equations describing a coating process with a heavy viscous incompressible fluid onto a horizontally moving rigid wall. One of the a priori unknown free surfaces is noncompact and the other free surface ends at an a priori unknown contact line on the right wall. The problem is considered in the plane \(\mathbb{R}^2\).

MSC:

35R35 Free boundary problems for PDEs
35Q30 Navier-Stokes equations
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