Premium
Three‐dimensional Navier‐Stokes‐Voight equation with a memory and the Brinkman‐Forchheimer damping term
Author(s) -
Wang Xiuqing,
Qin Yuming
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5710
Subject(s) - mathematics , attractor , nonlinear system , mathematical analysis , scaling , term (time) , exponential function , kernel (algebra) , physics , geometry , pure mathematics , quantum mechanics
In this paper, we consider the 3D Navier‐Stokes‐Voight model with a nonlinear damping, where the instantaneous kinematic viscosity is replaced by a memory through a distributed delay effect. We prove that the system possesses global and exponential attractors A ε , where ε ∈(0,1) is the scaling parameter in the memory kernel. We also prove that the model converges to the classical Navier‐Stokes‐Voight model with nonlinear damping when ε →0 as t → ∞ . Our results have extended those in Plinio et al.