Navier-Stokes flow down an inclined plane: Downward periodic motion
type: Item
instance of: scholarly article
title: Navier-Stokes flow down an inclined plane: Downward periodic motion
zbMATH Open document ID: 0815.76027
author: Takaaki Nishida
author: Yoshiaki Teramoto
author: Htay Aung Win
published in: Journal of Mathematics of Kyoto University
publication date: 1995-07-10T00:00:00Z
review text: Let us consider the motion of a viscous fluid stratum flowing on an inclined plane. Its bottom is at smooth contact with the plane, and its top is free. Let the fluid be subjected to the gravity force, so that the motion is due to the component of this force parallel to the inclined plane. A steady motion, defined by a constant velocity \(u_ 0\) parallel to the slope of the bottom, is a solution of the equations of the flow. Let us now suppose that another motion, periodic with period \(2\pi\) in the direction of the flow, may be superimposed on the fundamental steady motion. We aks whether such a motion is possible. The problem can be mathematically treated in the following way. Through a diffeomorphism we may reduce the domain to a stratum contained between two parallel planes. Let us also assume that the solution is smooth enough, although this restriction can be removed by using the method of mollification. Then we can derive a priori estimates, necessary for treating the Navier-Stokes equations. Under this respect, the paper is an application of a previous result by \textit{T. Nishida} [Commun. Pure Appl. Math. 39, Suppl., S221--S238 (1986; Zbl 0615.76078)].
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 567078
zbMATH Keywords: motion of stratum
zbMATH Keywords: diffeomorphism
zbMATH Keywords: method of mollification
zbMATH Keywords: a priori estimates
reviewed by: Piero Villaggio
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519193
OpenAlex ID: W1897178976
DOI: 10.1215/KJM/1250519193
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description: scientific article; zbMATH DE number 567078