Weak solutions to a two-phase thin film model with insoluble surfactant\n driven by capillary effects

2016/08/29 by Gabriele Bruell, Bruell, Gabriele
Computer Science · Engineering · Mathematics · #35D30 #35K41 #35K65 #35Q35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1608.07942

openalex publication_date 2016/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Of concern is the study of a system of three equations describing the motion\nof a viscous complete wetting two-phase thin film endowed with a layer of\ninsoluble surfactant on the surface of the upper fluid under the effects of\ncapillary forces. The governing equations for the film heights of the two-phase\nflow are degenerate, parabolic and strongly coupled fourth-order equations,\nwhich are additionally coupled to a second-order parabolic transport equation\nfor the surfactant concentration. A result on the existence of non-negative\nglobal weak solutions is presented.\n

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