This paper is concerned with a plane steady-state inclined film flow including evaporation effects. The motion is governed by a free boundary value problem for a coupled system of Navier–Stokes and Stefan equations. The flow domain is unbounded in two directions and it contains a geometrical perturbation on the inclined bottom. Existence and uniqueness of a suitable solution in weighted Sobolev spaces can be proved for small data (perturbation, inclination of the bottom) characterizing the problem.
Socolowsky, J. (2013). On a two-fluid inclined film flow with evaporation. Mathematical Modelling and Analysis, 18(1), 22-31. https://doi.org/10.3846/13926292.2013.756434
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