Open Access
Issue
Wuhan Univ. J. Nat. Sci.
Volume 28, Number 1, February 2023
Page(s) 1 - 10
DOI https://doi.org/10.1051/wujns/2023281001
Published online 17 March 2023
  1. Nield D A, Bejan A. Convection in Porous Media [M]. New York: Springer-Verlag , 1992. [CrossRef] [Google Scholar]
  2. Payne L E, Straughan B. Stability in the initial-time geometry problem for the Brinkman and Darcy equations of flow in a porous media [J]. Journal de Mathématiques Pures et Appliquées, 1996, 75(3): 225-271. [Google Scholar]
  3. Payne L E, Straughan B. Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modelling questions [J]. Journal de Mathématiques Pures et Appliquées, 1998, 77(4): 317-354. [CrossRef] [MathSciNet] [Google Scholar]
  4. Celebi A O, Kalantarov V, Ugurlu D. Continuous dependence for the convective Brinkman-Forchheimer equations [J]. Applicable Analysis, 2005, 84(9): 877-888. [CrossRef] [MathSciNet] [Google Scholar]
  5. Celebi A O, Kalantarov V, Ugurlu D. On continuous dependence on coefficients of the Brinkman Forchheimer equations [J]. Applied Mathematics Letters, 2006, 19(8): 801-807. [CrossRef] [MathSciNet] [Google Scholar]
  6. Liu Y. Convergence and continuous dependence for the Brinkman-Forchheimer equations [J]. Mathematical and Computer Modelling, 2009, 49(7-8): 1401-1415. [Google Scholar]
  7. Payne L E, Straughan B. Convergence and continuous dependence for the Brinkman-Forchheimer equations [J]. Studies in Applied Mathematics, 1999, 102(4): 419-439. [CrossRef] [MathSciNet] [Google Scholar]
  8. Liu Y, Xiao S Z, Lin Y W. Continuous dependence for the Brinkman-Forchheimer fluid inter facing with a Darcy fluid in a bounded domain [J]. Mathematics and Computers in Simulation, 2018, 150: 66-82. [CrossRef] [MathSciNet] [Google Scholar]
  9. Li Y F, Lin C H. Continuous dependence for the nonhomogeneous Brinkman-Forchheimer equations in a semi-infinitepipe [J]. Applied Mathematics and Computation , 2014, 244: 201-208. [CrossRef] [MathSciNet] [Google Scholar]
  10. Ugurlu D. On the existence of a global attractor for the Brinkman-Forchheimer equation [J]. Nonlinear Analysis: Theory, Methods & Applications, 2008, 68(7): 1986-1992. [CrossRef] [MathSciNet] [Google Scholar]
  11. Ouyang Y, Yang L E. A note on the existence of a global attractor for the Brinkman Forchheimer equations [J]. Nonlinear Analysis :Theory, Methods & Applications, 2009, 70(5): 2054-2059. [CrossRef] [MathSciNet] [Google Scholar]
  12. Wang B X, Lin S Y. Existence of global attractors for the three-dimensional Brinkman Forchheimer equations [J]. Mathematical Methods in the Applied Sciences, 2010, 31(12): 1479-1495. [Google Scholar]
  13. Song X L. Pullback D-attractors for a non-autonomous Brinkman-Forchheimer system [J]. Journal of Mathematical Research with Applications, 2013, 33(1): 90-100. [Google Scholar]
  14. Song X L, Xu S, Qiao B M. Formula - decay of solutions for the three-dimensional Brinkman Forchheimer equations in Formula [J] . Mathematics in Practice and Theory, 2020, 50(22): 307-314(Ch). [Google Scholar]
  15. Song X L, Wu J H. Non-autonomous 3D Brinman-Forchheimer equation with oscillating external force and its uniform attractor [J]. AIMS Mathematics, 2020, 5(2): 1484-1504. [CrossRef] [MathSciNet] [Google Scholar]
  16. Liu W J, Yang R, Yang X G. Dynamics of a 3D Brinman Forchheimer equation with infinite delay [J]. Communications on Pure and Applied Analysis, 2021, 20(5): 1907-1930. [CrossRef] [MathSciNet] [Google Scholar]
  17. Yang X G, Li L, Yan X J, et al. The structure and stability of pullback attractors for 3D Brinkman-Forchheimer equation with delay [J]. Electronic Research Archive, 2020, 28(4): 1395-1418. [CrossRef] [MathSciNet] [Google Scholar]
  18. Qiao B M, Li X F, Song X L. The existence of global attractors for the strong solutions of three-dimensional Brinkman Forchheimer equations [J]. Mathematics in Practice and Theory, 2020, 50(10): 238-251(Ch). [Google Scholar]
  19. Kalantarov V K, Titi E S. Global attractors and determining modes for the 3D Navier-Stokes-Voight equations [J]. Chinese Annals of Mathematics, Series B, 2009, 30(6): 697-714. [Google Scholar]
  20. Zelati M C, Gal C G. Singular limits of Voigt models in fluid dynamics [J]. Journal of Mathematical Fluid Mechanics, 2015, 17(2): 233-259. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  21. Mohan M T. Global and exponential attractors for the 3D Kelvin-Voigt-Brinkman Forchheimer equations [J]. Discrete and Continuous Dynamical Systems, Series B, 2020, 25(9): 3393-3436. [CrossRef] [MathSciNet] [Google Scholar]
  22. Ilyin A A. On the spectrum of the Stokes operator [J]. Functional Analysis and Its Applications, 2009, 43(4): 254-263. [CrossRef] [MathSciNet] [Google Scholar]
  23. Temam R H. Infinite-Dimensional Dynamical Systems in Mechanics and Physics[M]. New York: Springer-Verlag, 1997. [CrossRef] [Google Scholar]
  24. Cai X, Jiu Q. Weak and strong solutions for the incompressible Navier-Stokes equations with damping [J]. Journal of Mathematical Analysis and Applications, 2008, 343(2): 799-809. [Google Scholar]
  25. Kuang J C. Applied Inequalities [M]. Jinan: Shandong Science and Technology Press, 2010(Ch). [Google Scholar]
  26. Constantin P, Foias C. Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations [J]. Communications on Pure & Applied Mathematics, 1985, 38(1): 1-27. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]

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