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 | |
| Publication status | Published - 2016 Dec 1 |
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Keywords
- Burgers equation
- Free boundary problem
- Inclined plane
- Navier–Stokes equations
- Thin film approximation
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
A mathematical justification of a thin film approximation for the flow down an inclined plane. / Ueno, Hiroki; Iguchi, Tatsuo.
In: Journal of Mathematical Analysis and Applications, Vol. 444, No. 1, 01.12.2016, p. 804-824.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A mathematical justification of a thin film approximation for the flow down an inclined plane
AU - Ueno, Hiroki
AU - Iguchi, Tatsuo
PY - 2016/12/1
Y1 - 2016/12/1
N2 - 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.
AB - 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.
KW - Burgers equation
KW - Free boundary problem
KW - Inclined plane
KW - Navier–Stokes equations
KW - Thin film approximation
UR - http://www.scopus.com/inward/record.url?scp=84993968393&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84993968393&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2016.06.064
DO - 10.1016/j.jmaa.2016.06.064
M3 - Article
AN - SCOPUS:84993968393
VL - 444
SP - 804
EP - 824
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -