Spatial decay bounds for the channel flow of the Boussinesq equations

In this paper, we consider the Boussinesq equations in a semi-infinite channel. We show that, under appropriate restrictions on the data, if the fluid velocity initially is small, the solution will tend exponentially to a transient laminar flow as the distance from the entry section tends to infinit...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2011-09, Vol.381 (1), p.87-109
Main Authors: Liu, Yan, Li, Yuanfei, Lin, Yiwu, Yao, Zhengan
Format: Article
Language:English
Subjects:
Boussinesq equations
Decay bounds
Exact sciences and technology
Incompressible viscous fluid
Mathematical analysis
Mathematics
Saint-Venantʼs principle
Sciences and techniques of general use
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Summary:In this paper, we consider the Boussinesq equations in a semi-infinite channel. We show that, under appropriate restrictions on the data, if the fluid velocity initially is small, the solution will tend exponentially to a transient laminar flow as the distance from the entry section tends to infinity. We also derive the explicit decay bounds.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.02.066