Open Access
Wuhan Univ. J. Nat. Sci.
Volume 28, Number 4, August 2023
Page(s) 282 - 290
Published online 06 September 2023
  1. Firdaouss M, Guermond J L, Le Quéré P. Nonlinear corrections to Darcy's law at low Reynolds numbers [J]. Journal of Fluid Mechanics, 1997, 343: 331-350. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  2. Whitaker S. The Forchheimer equation: A theoretical development [J]. Transport in Porous Media, 1996, 25(1): 27-61. [Google Scholar]
  3. Qin Y, Kaloni P N. Spatial decay estimates for plane flow in Brinkman-Forchheimer model [J]. Quarterly of Applied Mathematics, 1998, 56(1): 71-87. [CrossRef] [MathSciNet] [Google Scholar]
  4. Kaloni P N, Guo J L. Steady nonlinear double-diffusive convection in a porous medium based upon the brinkman-forchheimer model [J]. Journal of Mathematical Analysis and Applications, 1996, 204(1): 138-155. [CrossRef] [MathSciNet] [Google Scholar]
  5. Payne L E, Song J C, Straughan B. Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity [J]. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 1999, 455(1986): 2173-2190. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  6. Liu Y. Convergence and continuous dependence for the Brinkman-Forchheimer equations[J]. Math Comput Modelling, 2009, 49(7-8): 1401-1415. [CrossRef] [MathSciNet] [Google Scholar]
  7. Givler R C, Altobelli S A. A determination of the effective viscosity for the Brinkman-Forchheimer flow model[J]. Journal of Fluid Mechanics, 1994, 258: 355-370. [NASA ADS] [CrossRef] [Google Scholar]
  8. Nield D A. The limitations of the Brinkman-Forchheimer equation in modeling flow in a saturated porous medium and at an interface [J]. International Journal of Heat and Fluid Flow, 1991, 12(3): 269-272. [CrossRef] [Google Scholar]
  9. Vafai K, Kim S J. Fluid mechanics of the interface region between a porous medium and a fluid layer—An exact solution[J]. International Journal of Heat and Fluid Flow, 1990, 11(3): 254-256. [CrossRef] [Google Scholar]
  10. Vafai K, Kim S J. On the limitations of the Brinkman-Forchheimer-extended Darcy equation[J]. International Journal of Heat and Fluid Flow, 1995, 16(1): 11-15. [NASA ADS] [CrossRef] [Google Scholar]
  11. Uğurlu D. On the existence of a global attractor for the Brinkman-Forchheimer equations[J]. Nonlinear Analysis: Theory, Methods & Applications, 2008, 68(7): 1986-1992. [CrossRef] [MathSciNet] [Google Scholar]
  12. 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]
  13. Song X L. Pullback D-attractors for a non-autonomous Brinkman-Forchheimer system[J]. J Math Res Appl, 2013, 33(1): 90-100. [MathSciNet] [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]. Math Pract Theory, 2020, 50(22): 307-314. [Google Scholar]
  15. 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]. Math Pract Theory, 2020, 50(10): 238-251. [Google Scholar]
  16. Song X L, Wu J H. Non-autonomous 3D Brinkman-Forchheimer equation with singularly oscillating external force and its uniform attractor[J]. AIMS Mathematics, 2020, 5(2): 1484-1504. [CrossRef] [MathSciNet] [Google Scholar]
  17. Wang B X. Attractors for reaction-diffusion equations in unbounded domains[J]. Physica D: Nonlinear Phenomena, 1999, 128(1): 41-52. [CrossRef] [MathSciNet] [Google Scholar]
  18. Contantin P, Foias C. Navier-Stokes equations[C]// Chicago Lect Math. Chicago: University of Chicago Press, 1988. [Google Scholar]
  19. Temam T. Navier-Stokes Equations: Teory and Numerical Analysis[M]. Amsterdam: North-Holland, 1979. [Google Scholar]
  20. Fucci G, Wang B X, Singh P. Asymptotic behavior of the Newton-Boussinesq equation in a two-dimensional channel[J]. Nonlinear Analysis: Theory, Methods & Applications, 2009, 70(5): 2000-2013. [CrossRef] [MathSciNet] [Google Scholar]
  21. Babin A V, Vishik M I. Attractors of Evolution Equation[M]. Amsterdam: North-Holland, 1992. [Google Scholar]
  22. Ball J M. Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations[J]. Journal of Nonlinear Science, 1997, 7(5): 475-502. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  23. Hale J. Asymptotic Behavior of Dissipative Systems[M]. Providence, Rhode Island: American Mathematical Society, 2010. [CrossRef] [Google Scholar]
  24. Sell G R, You Y C. Dynamics of Evolutionary Equations[M]. New York: Springer-Verlag, 2002. [CrossRef] [Google Scholar]
  25. Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics[M]. New York: Springer-Verlag, 1997. [CrossRef] [Google Scholar]

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