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On periodic Stokesian Hele-Shaw flows with surface tension

Published online by Cambridge University Press:  01 December 2008

J. ESCHER  and
B.-V. MATIOC
J. ESCHER
Affiliation:
Institute of Applied Mathematics, Leibniz University of Hanover, Welfengarten 1, D-30167 Hanover, Germany email: escher@ifam.uni-hannover.de; matioc@ifam.uni-hannover.de
B.-V. MATIOC
Affiliation:
Institute of Applied Mathematics, Leibniz University of Hanover, Welfengarten 1, D-30167 Hanover, Germany email: escher@ifam.uni-hannover.de; matioc@ifam.uni-hannover.de
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Abstract

In this paper we consider a 2π-periodic and two-dimensional Hele-Shaw flow describing the motion of a viscous, incompressible fluid. The free surface is moving under the influence of surface tension and gravity. The motion of the fluid is modelled using a modified version of Darcy's law for Stokesian fluids. The bottom of the cell is assumed to be impermeable. We prove the existence of a unique classical solution for a domain which is a small perturbation of a cylinder. Moreover, we identify the equilibria of the flow and study their stability.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 19 , Issue 6 , December 2008 , pp. 717 - 734
Copyright
Copyright © Cambridge University Press 2008

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