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

Hiroki Ueno, Tatsuo Iguchi

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)804-824
ページ数21
ジャーナルJournal of Mathematical Analysis and Applications
444
1
DOI
出版ステータスPublished - 2016 12 1

ASJC Scopus subject areas

  • 分析
  • 応用数学

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