JournalsifbVol. 11, No. 1pp. 119–137

A moving boundary problem for periodic Stokesian Hele–Shaw flows

  • Joachim Escher

    University of Hannover, Germany
  • Bogdan-Vasile Matioc

    Leibniz University Hannover, Germany
A moving boundary problem for periodic Stokesian Hele–Shaw flows cover
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Abstract

This paper is concerned with the motion of an incompressible, viscous fluid in a Hele-Shaw cell. The free surface is moving under the influence of gravity and the fluid is modelled using a modified Darcy law for Stokesian fluids. We combine results from the theory of quasilinear elliptic equations, analytic semigroups and Fourier multipliers to prove existence of a unique classical solution to the corresponding moving boundary problem.

Cite this article

Joachim Escher, Bogdan-Vasile Matioc, A moving boundary problem for periodic Stokesian Hele–Shaw flows. Interfaces Free Bound. 11 (2009), no. 1, pp. 119–137

DOI 10.4171/IFB/205