Details
Original language | English |
---|---|
Pages (from-to) | 1992-2006 |
Number of pages | 15 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 40 |
Issue number | 5 |
Publication status | Published - 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
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Mathematical Analysis, Vol. 40, No. 5, 10.2009, p. 1992-2006.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Existence and stability results for periodic stokesian hele-shaw flows
AU - Escher, Joachim
AU - Matioc, Bogdan-Vasile
PY - 2009/10
Y1 - 2009/10
N2 - 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.
AB - 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.
KW - Hele-Shaw flow
KW - Non Newtonian fluid
KW - Nonlinear parabolic equation
KW - Oldroyd-B fluid
KW - Power law fluid
KW - Quasi-linear elliptic equation
UR - http://www.scopus.com/inward/record.url?scp=70350102573&partnerID=8YFLogxK
U2 - 10.1137/070707671
DO - 10.1137/070707671
M3 - Article
AN - SCOPUS:70350102573
VL - 40
SP - 1992
EP - 2006
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 5
ER -