Uniform estimates for the flow of a viscous incompressible fluid down an inclined plane in the thin film regime

Hiroki Ueno, Akinori Shiraishi, 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, it is hard to treat the Navier-Stokes equations directly, so that a thin film approximation is often used. It is an approximation obtained by the perturbation expansion with respect to the aspect ratio δ of the film under the thin film regime δ. ≪ 1. Our purpose is to give a mathematically rigorous justification of the thin film approximation by establishing an error estimate between the solution of the Navier-Stokes equations and those of approximate equations. To this end, in this paper we derive a uniform estimate for the solution of the Navier-Stokes equations with respect to δ under appropriate assumptions.

本文言語English
ページ(範囲)248-287
ページ数40
ジャーナルJournal of Mathematical Analysis and Applications
436
1
DOI
出版ステータスPublished - 2016 4 1

ASJC Scopus subject areas

  • 分析
  • 応用数学

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