On a Two-Fluid Inclined Film Flow with Evaporation

Abstract

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.

Keywords:

• Navier–Stokes equations
• Stefan equations
• evaporation
• free boundary value problem
• perturbed bottom

AMS Subject Classification:

• 35R35
• 35Q30
• 76D03
• 76D05