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Boundary layer associated with the Darcy-Brinkman-Boussinesq model for convection in porous media. (English) Zbl 1209.37102

Summary: We study the asymptotic behavior of the infinite Darcy-Prandtl number Darcy-Brinkman-Boussinesq system for convection in porous media at a small Brinkman-Darcy number. The existence of a boundary layer with thickness proportional to the square root of the Brinkman-Darcy number for the velocity field is established in both the \(L^\infty (H^{1})\) norm (in 2D and 3D) and the \(L^\infty (L^\infty )\) norm (in 2D). This improves in several respects an earlier result of L. E. Payne and B. Straughan [J. Math. Pures Appl., IX. Sér. 77, No. 4, 317–354 (1998; Zbl 0906.35067)] where the vanishing Brinkman-Darcy number limit is studied without resolving the boundary layer.

MSC:

37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76S05 Flows in porous media; filtration; seepage
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q35 PDEs in connection with fluid mechanics

Citations:

Zbl 0906.35067
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