Fractal and Fractional (Feb 2023)

Determination of Three-Dimensional Brinkman—Forchheimer-Extended Darcy Flow

  • Zhengwang Tao,
  • Xin-Guang Yang,
  • Yan Lin,
  • Chunxiao Guo

DOI
https://doi.org/10.3390/fractalfract7020146
Journal volume & issue
Vol. 7, no. 2
p. 146

Abstract

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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.

Keywords