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Structural stability of the Boussinesq fluid interfacing with a Darcy fluid in a bounded region in R2

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  • Liu, Yan
  • Qin, Xulong
  • Shi, Jincheng
  • Zhi, Wenjing

Abstract

The structural stability of the Boussinesq fluid interfacing with a Darcy fluid in a bounded region in R2 was studied. We assumed that the viscous fluid was governed by the Boussinesq equations in Ω1, while in Ω2, we supposed that the flow satisfies the Darcy equations. Some interfacing boundary conditions are imposed. The traditional Poincare´ inequalities can’t be used. With the aid of some useful a priori bounds and some new Poincare´ inequalities, we were able to demonstrate the continuous dependence result on the interface coefficient α. The result showed that the structural stability is valid for the interfacing problem.

Suggested Citation

  • Liu, Yan & Qin, Xulong & Shi, Jincheng & Zhi, Wenjing, 2021. "Structural stability of the Boussinesq fluid interfacing with a Darcy fluid in a bounded region in R2," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    • Handle: RePEc:eee:apmaco:v:411:y:2021:i:c:s0096300321005774
    DOI: 10.1016/j.amc.2021.126488
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    References listed on IDEAS

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    1. Liu, Yan & Xiao, Shengzhong & Lin, Yiwu, 2018. "Continuous dependence for the Brinkman–Forchheimer fluid interfacing with a Darcy fluid in a bounded domain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 150(C), pages 66-82.
    2. Liu, Yan, 2017. "Continuous dependence for a thermal convection model with temperature-dependent solubility," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 18-30.
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    Cited by:

    1. Zhanwei Guo & Jincheng Shi & Danping Ding, 2022. "Convergence of the Boundary Parameter for the Three-Dimensional Viscous Primitive Equations of Large-Scale," Mathematics, MDPI, vol. 10(21), pages 1-11, November.

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    3. Zhanwei Guo & Jincheng Shi & Danping Ding, 2022. "Convergence of the Boundary Parameter for the Three-Dimensional Viscous Primitive Equations of Large-Scale," Mathematics, MDPI, vol. 10(21), pages 1-11, November.

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