Structural stability for the Boussinesq equations interfacing with Darcy equations in a bounded domain

A priori bounds were derived for the flow in a bounded domain for the viscous-porous interfacing fluids. We assumed that the viscous fluid was slow in Ω 1 , which was governed by the Boussinesq equations. For a porous medium in Ω 2 , we supposed that the flow satisfied the Darcy equations. With the...

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Bibliographic Details
Published in:Boundary value problems 2021-03, Vol.2021 (1), p.1-19, Article 27
Main Authors: Li, Yuanfei, Zhang, Shuanghu, Lin, Changhao
Format: Article
Language:English
Subjects:
A priori bounds
Analysis
Approximations and Expansions
Boussinesq coefficient
Boussinesq equations
Continuous dependence
Darcys law
Difference and Functional Equations
Domains
Interface stability
Interfacing problem
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Porous media
Structural stability
Viscous fluids
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Summary:A priori bounds were derived for the flow in a bounded domain for the viscous-porous interfacing fluids. We assumed that the viscous fluid was slow in Ω 1 , which was governed by the Boussinesq equations. For a porous medium in Ω 2 , we supposed that the flow satisfied the Darcy equations. With the aid of these a priori bounds we were able to demonstrate the result of the continuous dependence type for the Boussinesq coefficient λ . Following the method of a first-order differential inequality, we can further obtain the result that the solution depends continuously on the interface boundary coefficient α . These results showed that the structural stability is valid for the interfacing problem.
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-021-01501-0