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The existence of uniform attractors for the 3D micropolar equations with nonlinear damping term
AIMS Mathematics 2024, 9(4): 9608-9630
Published: 15 April 2024
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This paper studies the existence of uniform attractors for 3D micropolar equation with damping term. When β > 3, with initial data ( u τ , ω τ ) V 1 × V 2 and external forces ( f 1 , f 2 ) H ( f 1 0 ) × H ( f 2 0 ), some uniform estimates of the solution in different function spaces are given. Based on these uniform estimates, the ( ( V 1 × V 2 ) × ( H ( f 1 0 ) × H ( f 2 0 ) ) , V 1 × V 2 )-continuity of the family of processes { U ( f 1 , f 2 ) ( t , τ ) } t τ is demonstrated. Meanwhile, the ( V 1 × V 2 , H 2 ( Ω ) × H 2 ( Ω ) )-uniform compactness of { U ( f 1 , f 2 ) ( t , τ ) } t τ is proved. Finally, the existence of a ( V 1 × V 2 , V 1 × V 2 )-uniform attractor and a ( V 1 × V 2 , H 2 ( Ω ) × H 2 ( Ω ) )-uniform attractor are obtained. Furthermore, the ( V 1 × V 2 , V 1 × V 2 )-uniform attractor and the ( V 1 × V 2 , H 2 ( Ω ) × H 2 ( Ω ) )-uniform attractor are verified to be the same.

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