Open AccessON A TWO-FLUID INCLINED FILM FLOW WITH EVAPORATION
Author(s) -
Jürgen Socolowsky
Publication year - 2013
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2013.756434
Subject(s) - uniqueness , inclined plane , perturbation (astronomy) , mathematics , sobolev space , boundary value problem , mathematical analysis , flow (mathematics) , evaporation , mechanics , geometry , physics , thermodynamics , quantum mechanics
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.