Existence and stability results for periodic stokesian hele-shaw flows

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Original languageEnglish
Pages (from-to)1992-2006
Number of pages15
JournalSIAM Journal on Mathematical Analysis
Volume40
Issue number5
Publication statusPublished - Oct 2009

Abstract

We consider here a? 2π-periodic and two-dimensional Hele-Shaw flow modelling the motion of a viscous and incompressible fluid. The free surface is moving under the influence of gravity and is modelled by a modified Darcy law for Stokesian fluids. The bottom of the cell is assumed to be impermeable. We prove the existence of a unique classical solution if the initial data is near a constant, identify the equilibria of the flow, and study their stability.

Keywords

    Hele-Shaw flow, Non Newtonian fluid, Nonlinear parabolic equation, Oldroyd-B fluid, Power law fluid, Quasi-linear elliptic equation

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Existence and stability results for periodic stokesian hele-shaw flows. / Escher, Joachim; Matioc, Bogdan-Vasile.
In: SIAM Journal on Mathematical Analysis, Vol. 40, No. 5, 10.2009, p. 1992-2006.

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