Summary: "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 twop-hase 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 semigroup 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.''
%0 Journal Article
%1 MR4373882
%A Assenmacher, Oliver
%A Bruell, Gabriele
%A Lienstromberg, Christina
%D 2022
%J Comm. Partial Differential Equations
%K Lienstromberg from:elkepeter non-Newtonian film thin
%N 1
%P 197--232
%R 10.1080/03605302.2021.1957929
%T Non-Newtonian two-phase thin-film problem: local existence,
uniqueness, and stability
%U https://doi.org/10.1080/03605302.2021.1957929
%V 47
%X Summary: "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 twop-hase 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 semigroup 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.''
@article{MR4373882,
abstract = {Summary: "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 twop-hase 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 semigroup 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.''},
added-at = {2023-03-14T08:16:03.000+0100},
author = {Assenmacher, Oliver and Bruell, Gabriele and Lienstromberg, Christina},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2c7341805c058b850f13c6365ba101f06/mathematik},
doi = {10.1080/03605302.2021.1957929},
fjournal = {Communications in Partial Differential Equations},
interhash = {436c4029d801256546dc1ca113ef1393},
intrahash = {c7341805c058b850f13c6365ba101f06},
issn = {0360-5302},
journal = {Comm. Partial Differential Equations},
keywords = {Lienstromberg from:elkepeter non-Newtonian film thin},
mrclass = {76A05 (35B40 35K41 35K65 35Q35 76A20)},
mrnumber = {4373882},
number = 1,
pages = {197--232},
timestamp = {2023-12-05T17:17:35.000+0100},
title = {Non-{N}ewtonian two-phase thin-film problem: local existence,
uniqueness, and stability},
url = {https://doi.org/10.1080/03605302.2021.1957929},
volume = 47,
year = 2022
}
