Details
| Original language | English |
|---|---|
| Pages (from-to) | 513-522 |
| Number of pages | 10 |
| Journal | Journal of Evolution Equations |
| Volume | 8 |
| Issue number | 3 |
| Publication status | Published - 9 Jul 2008 |
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.
Keywords
- Hele-Shaw flow, Non-Newtonian fluid, Nonlinear parabolic equation, Steady state
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics (miscellaneous)
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In: Journal of Evolution Equations, Vol. 8, No. 3, 09.07.2008, p. 513-522.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Stability of the equilibria for periodic Stokesian Hele-Shaw flows
AU - Escher, Joachim
AU - Matioc, Bogdan-Vasile
PY - 2008/7/9
Y1 - 2008/7/9
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 - http://www.scopus.com/inward/record.url?scp=50849131201&partnerID=8YFLogxK
U2 - 10.1007/s00028-008-0381-8
DO - 10.1007/s00028-008-0381-8
M3 - Article
AN - SCOPUS:50849131201
VL - 8
SP - 513
EP - 522
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
SN - 1424-3199
IS - 3
ER -