Stability of the equilibria for periodic Stokesian Hele-Shaw flows

Joachim Escher; Bogdan-Vasile Matioc

doi:10.1007/s00028-008-0381-8

Stability of the equilibria for periodic Stokesian Hele-Shaw flows

Joachim Escher^*
, Bogdan-Vasile Matioc

^*Corresponding author for this work

Institute of Applied Mathematics

Research output: Contribution to journal › Article › Research › peer review

Abstract

In this paper we consider the 2-dimensional flow of a Stokesian fluid in a Hele-Shaw cell. The motion of the flow is modelled by a modified Darcy's law. The existence of local solutions has been proved by the authors in a recent work, cf. [4]. The purpose of this paper is to identify the steady states of this flow and to study their stability. The equilibria will be identified as solutions of elliptic free boundary problems. It is shown that if the pressure on the bottom is constant then the corresponding steady state is asymptotically stable.

Original language	English
Pages (from-to)	513-522
Number of pages	10
Journal	Journal of Evolution Equations
Volume	8
Issue number	3
DOIs	https://doi.org/10.1007/s00028-008-0381-8
Publication status	Published - 9 Jul 2008

Keywords

Hele-Shaw flow
Non-Newtonian fluid
Nonlinear parabolic equation
Steady state

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1007/s00028-008-0381-8

Cite this

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abstract = "In this paper we consider the 2-dimensional flow of a Stokesian fluid in a Hele-Shaw cell. The motion of the flow is modelled by a modified Darcy's law. The existence of local solutions has been proved by the authors in a recent work, cf. [4]. The purpose of this paper is to identify the steady states of this flow and to study their stability. The equilibria will be identified as solutions of elliptic free boundary problems. It is shown that if the pressure on the bottom is constant then the corresponding steady state is asymptotically stable.",

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AU - Matioc, Bogdan-Vasile

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N2 - In this paper we consider the 2-dimensional flow of a Stokesian fluid in a Hele-Shaw cell. The motion of the flow is modelled by a modified Darcy's law. The existence of local solutions has been proved by the authors in a recent work, cf. [4]. The purpose of this paper is to identify the steady states of this flow and to study their stability. The equilibria will be identified as solutions of elliptic free boundary problems. It is shown that if the pressure on the bottom is constant then the corresponding steady state is asymptotically stable.

AB - In this paper we consider the 2-dimensional flow of a Stokesian fluid in a Hele-Shaw cell. The motion of the flow is modelled by a modified Darcy's law. The existence of local solutions has been proved by the authors in a recent work, cf. [4]. The purpose of this paper is to identify the steady states of this flow and to study their stability. The equilibria will be identified as solutions of elliptic free boundary problems. It is shown that if the pressure on the bottom is constant then the corresponding steady state is asymptotically stable.

KW - Hele-Shaw flow

KW - Non-Newtonian fluid

KW - Nonlinear parabolic equation

KW - Steady state

UR - https://www.scopus.com/pages/publications/50849131201

U2 - 10.1007/s00028-008-0381-8

DO - 10.1007/s00028-008-0381-8

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VL - 8

SP - 513

EP - 522

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

IS - 3

ER -

Stability of the equilibria for periodic Stokesian Hele-Shaw flows

Abstract

Keywords

ASJC Scopus subject areas

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