Dynamics of the three-dimensional Brinkman-Forchheimer-extended Darcy model in the whole space. (English) Zbl 1534.35039
Summary: This paper is concerned with the pullback dynamics of a three-dimensional Brinkman-Forchheimer-extended Darcy (3D BFeD) model for porous media in the whole space. The existence and uniqueness of weak solutions is achieved firstly, leading to the generation of a continuous non-autonomous cocycle for the BFed model. Based on the global well-posedness, the existence of pullback attractors is proved by using uniform a priori estimates on the tails of solutions outside bounded domains.
MSC:
| 35B41 | Attractors |
| 35Q30 | Navier-Stokes equations |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
Brinkman-Forchheimer-extended Darcy model; whole space; well-posedness; tail estimates of solutions; pullback attractorsReferences:
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