Thin-film approximations of the two-phase Stokes problem

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OriginalspracheEnglisch
Seiten (von - bis)1-13
Seitenumfang13
FachzeitschriftNonlinear Analysis, Theory, Methods and Applications
Jahrgang76
Ausgabenummer1
PublikationsstatusVeröffentlicht - 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.

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Thin-film approximations of the two-phase Stokes problem. / Escher, Joachim; Matioc, Anca Voichita; Matioc, Bogdan-Vasile.
in: Nonlinear Analysis, Theory, Methods and Applications, Jahrgang 76, Nr. 1, 01.2013, S. 1-13.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Escher J, Matioc AV, Matioc BV. Thin-film approximations of the two-phase Stokes problem. Nonlinear Analysis, Theory, Methods and Applications. 2013 Jan;76(1):1-13. doi: 10.1016/j.na.2012.07.034
Escher, Joachim ; Matioc, Anca Voichita ; Matioc, Bogdan-Vasile. / Thin-film approximations of the two-phase Stokes problem. in: Nonlinear Analysis, Theory, Methods and Applications. 2013 ; Jahrgang 76, Nr. 1. S. 1-13.
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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 .

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KW - Degenerate parabolic system

KW - Exponential stability

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