KIT | KIT-Bibliothek | Impressum | Datenschutz

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

Assenmacher, Oliver; Bruell, Gabriele; Lienstromberg, Christina

Abstract:
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.

Open Access Logo


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
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page