Stationary Marangoni convection: a free boundary value problem for the Navier Stokes equations

Abstract

The author considers a stationary free boundary problem for the Navier Stokes system and the heat equation. The system is considered as a model for the motion of a fluid drop in a zero gravity field. The shape of the drop and the flow resp. pressure inside are determined by surface forces (at least in the case f = 0) and they act via a variable surface tension on the fluid inside. More precisely, a force on the surface (in our case it will be the gradient of a temperature field) changes the surface tension and the boundary conditions tell us how this causes an onset of a motion of the fluid inside. The system is written here in dimensionless form. In this paper the author proves existence and regularity of a solution of the stationary system. He decomposes the system in two systems. The first system contains the physical equations and the geometry is given, while the second one determines the geometry and the physical quantities are given. The paper is based on results, obtained by different authors in the last few years. (orig./AKF)SIGLEAvailable from TIB Hannover: RR 1606(94-41) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman