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Non-Newtonian two-phase thin-film problem: local existence, uniqueness, and stability

Assenmacher, Oliver; Bruell, Gabriele; Lienstromberg, Christina

We study the flow of two immiscible fluids located on a solid bottom, where the lower fluid is Newtonian and the upper fluid is a non-Newtonian Ellis fluid. Neglecting gravitational effects, we consider the formal asymptotic limit of small film heights in the two-phase Navier–Stokes system. This leads to a strongly coupled system of two parabolic equations of fourth order with merely Hölder-continuous dependence on the coefficients. For the case of strictly positive initial film heights we prove local existence of strong solutions by abstract semi-group theory. Uniqueness is proved by energy methods. Under additional regularity assumptions, we investigate asymptotic stability of the unique equilibrium solution, which is given by constant film heights.

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Volltext §
DOI: 10.5445/IR/1000129180
Veröffentlicht am 01.02.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 01.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000129180
Verlag KIT, Karlsruhe
Umfang 29 S.
Serie CRC 1173 Preprint ; 2021/4
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter non-Newtonian fluid, thin-film equation, two-phase flow, degenerate parabolic system, local existence and uniqueness, long-time asymptotics
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