A mathematical justification of a thin film approximation for the flow down an inclined plane

Hiroki Ueno; Tatsuo Iguchi

doi:10.1016/j.jmaa.2016.06.064

A mathematical justification of a thin film approximation for the flow down an inclined plane

Hiroki Ueno, Tatsuo Iguchi

Department of Mathematics

Research output: Contribution to journal › Article

2 Citations (Scopus)

Abstract

We consider a two-dimensional motion of a thin film flowing down an inclined plane under the influence of the gravity and the surface tension. In order to investigate the stability of such flow, we often use a thin film approximation, which is an approximation obtained by the perturbation expansion with respect to the aspect ratio of the film. The famous examples of the approximate equations are the Burgers equation, Kuramoto–Sivashinsky equation, KdV–Burgers equation, KdV–Kuramoto–Sivashinsky equation, and so on. In this paper, we give a mathematically rigorous justification of a thin film approximation by establishing an error estimate between the solution of the Navier–Stokes equations and those of approximate equations.

Original language	English
Pages (from-to)	804-824
Number of pages	21
Journal	Journal of Mathematical Analysis and Applications
Volume	444
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2016.06.064
Publication status	Published - 2016 Dec 1

Keywords

Burgers equation
Free boundary problem
Inclined plane
Navier–Stokes equations
Thin film approximation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2016.06.064

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Ueno, H., & Iguchi, T. (2016). A mathematical justification of a thin film approximation for the flow down an inclined plane. Journal of Mathematical Analysis and Applications, 444(1), 804-824. https://doi.org/10.1016/j.jmaa.2016.06.064

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