Details
| Original language | English |
|---|---|
| Pages (from-to) | 1-13 |
| Number of pages | 13 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 76 |
| Issue number | 1 |
| Publication status | Published - Jan 2013 |
Abstract
Passing to the limit of small layer thickness in the two-phase Stokes problem we obtain when including only gravity (resp. surface tension) effects a strongly coupled parabolic system of second (resp. fourth) order. In the non-degenerate case we prove that the corresponding evolution problems are locally well-posed. For the gravity driven flow though, we have to assume that the less dense fluid lies on top of the less dense layer. Moreover, we show that the solutions converge exponentially fast towards a flat steady-state, which is uniquely determined by the volume of the two fluids, provided they are initially close to this rest state.
Keywords
- Degenerate parabolic system, Exponential stability, Strong solution, Thin-film
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 76, No. 1, 01.2013, p. 1-13.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Thin-film approximations of the two-phase Stokes problem
AU - Escher, Joachim
AU - Matioc, Anca Voichita
AU - Matioc, Bogdan-Vasile
N1 - Funding information: Partially supported by the German Research Foundation (DFG) under the grant ES 195/5-1 .
PY - 2013/1
Y1 - 2013/1
N2 - Passing to the limit of small layer thickness in the two-phase Stokes problem we obtain when including only gravity (resp. surface tension) effects a strongly coupled parabolic system of second (resp. fourth) order. In the non-degenerate case we prove that the corresponding evolution problems are locally well-posed. For the gravity driven flow though, we have to assume that the less dense fluid lies on top of the less dense layer. Moreover, we show that the solutions converge exponentially fast towards a flat steady-state, which is uniquely determined by the volume of the two fluids, provided they are initially close to this rest state.
AB - Passing to the limit of small layer thickness in the two-phase Stokes problem we obtain when including only gravity (resp. surface tension) effects a strongly coupled parabolic system of second (resp. fourth) order. In the non-degenerate case we prove that the corresponding evolution problems are locally well-posed. For the gravity driven flow though, we have to assume that the less dense fluid lies on top of the less dense layer. Moreover, we show that the solutions converge exponentially fast towards a flat steady-state, which is uniquely determined by the volume of the two fluids, provided they are initially close to this rest state.
KW - Degenerate parabolic system
KW - Exponential stability
KW - Strong solution
KW - Thin-film
UR - http://www.scopus.com/inward/record.url?scp=84867051949&partnerID=8YFLogxK
U2 - 10.1016/j.na.2012.07.034
DO - 10.1016/j.na.2012.07.034
M3 - Article
AN - SCOPUS:84867051949
VL - 76
SP - 1
EP - 13
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 1
ER -