Fractal Fract, Vol. 7, Pages 146: Determination of Three-Dimensional Brinkman—Forchheimer-Extended Darcy Flow

Fractal Fract, Vol. 7, Pages 146: Determination of Three-Dimensional Brinkman—Forchheimer-Extended Darcy Flow

Fractal and Fractional doi: 10.3390/fractalfract7020146

Authors: Zhengwang Tao Xin-Guang Yang Yan Lin Chunxiao Guo

The aim of this study is to determine a 3D incompressible Brinkman–Forchheimer-extended Darcy fluid flow. Based on global well-posedness and regularity of solutions with a periodic boundary condition, the determining modes for weak and regular solutions is achieved via the generalized Grashof number for a 3D non-autonomous Brinkman–Forchheimer-Darcy fluid flow in porous medium. Furthermore, the asymptotic determination of the complete trajectories inside an attractor via Fourier functionals is shown for a 3D autonomous Brinkman–Forchheimer-extended Darcy model.