In this paper, we consider the long‐time behavior of weak solutions for the 2D autonomous non‐Newtonian micropolar fluids. By means of the method of ℓ‐trajectories introduced by Málek and Pražák, we first establish the existence of global attractor for solution semigroup {S(t)}t ≥ 0 associated with (1)–(3) and estimate the fractal dimension of global attractor in H × L2(Ω) is finite. Then we derive the existence of exponential attractor for solution semigroup {S(t)}t ≥ 0 associated with (1.1)‐(1.3) in H × L2(Ω).
This paper studies the long time behavior of the solution to the initial boundaryvalue problems for a class of strongly damped Kirchho type wave equations:utt "1ut + j ut jp1 ut + j u jq1 u (kruk2)u = f(x):Firstly, we prove the existence and uniqueness of the solution by priori estimate and the Galerkin method. Then we obtain to the existence of the global attractor. Finally, we consider that the estimation of the upper bounds of Hausdor and fractal dimensionsfor the global attractor is obtained.
In this paper, using the Gromov-Hausdorff distances between two global attractors (which may be in disjoint phase spaces) and two semi-dynamical systems introduced by Lee et al. ( 2020), we consider the continuous dependence of the global attractors and the stability of the semi-dynamical systems on global attractors induced by the Brinkman-Forchheimer equation under variation of the domain. The results of this paper improve on previous results, which can compare any two systems in different phase spaces without the process of "pull-backing" the perturbed systems to the original domain.
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