Open Access
Issue
Wuhan Univ. J. Nat. Sci.
Volume 28, Number 4, August 2023
Page(s) 282 - 290
DOI https://doi.org/10.1051/wujns/2023284282
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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.