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The boundedness and upper semicontinuity of the pullback attractors for a 2D micropolar fluid flows with delay

  • Received: 01 February 2020 Revised: 01 May 2020
  • Primary: 35B40, 35Q35; Secondary: 35B41

  • In this paper, two properties of the pullback attractor for a 2D non-autonomous micropolar fluid flows with delay on unbounded domains are investigated. First, we establish the $ H^1 $-boundedness of the pullback attractor. Further, with an additional regularity limit on the force and moment with respect to time t, we remark the $ H^2 $-boundedness of the pullback attractor. Then, we verify the upper semicontinuity of the pullback attractor with respect to the domains.

    Citation: Wenlong Sun. The boundedness and upper semicontinuity of the pullback attractors for a 2D micropolar fluid flows with delay[J]. Electronic Research Archive, 2020, 28(3): 1343-1356. doi: 10.3934/era.2020071

    Related Papers:

  • In this paper, two properties of the pullback attractor for a 2D non-autonomous micropolar fluid flows with delay on unbounded domains are investigated. First, we establish the $ H^1 $-boundedness of the pullback attractor. Further, with an additional regularity limit on the force and moment with respect to time t, we remark the $ H^2 $-boundedness of the pullback attractor. Then, we verify the upper semicontinuity of the pullback attractor with respect to the domains.



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    [1] Existence of $H^2$-global attractors of two-dimensional micropolar fluid flows. J. Math. Anal. Appl. (2006) 322: 512-522.
    [2] Uniform attractors of non-homogeneous micropolar fluid flows in non-smooth domains. Nonlinearity (2007) 20: 1619-1635.
    [3] Global attractors of two-dimensional micropolar fluid flows in some unbounded domains. Appl. Math. Comput. (2006) 182: 610-620.
    [4] Theory of micropolar fluids. J. Math. Mech. (1966) 16: 1-18.
    [5] $H^2$-boundedness of the pullback attractors for non-autonomous 2D Navier-Stokes equations in bounded domains. Nonlinear Anal. (2011) 74: 4882-4887.
    [6] G. Łukaszewicz, Micropolar Fluids. Theory and Applications, Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, Inc., Boston, MA, 1999. doi: 10.1007/978-1-4612-0641-5
    [7] Long time behavior of 2D micropolar fluid flows. Math. Comput. Modelling (2001) 34: 487-509.
    [8] Uniform attractor for 2D magneto-micropolar fluid flow in some unbounded domains. Z. Angew. Math. Phys. (2004) 55: 247-257.
    [9] On $H^1$-pullback attractors for nonautonomous micropolar fluid equations in a bounded domain. Nonlinear Anal. (2009) 71: 782-788.
    [10] Feedback controllers for a wind tunnel model involving a delay: Analytical design and numerical simulation. IEEE Trans. Automat. Control (1984) 29: 1058-1068.
    [11] Attractors for 2D-Navier-Stokes equations with delays on some unbounded domains. Nonlinear Anal. (2007) 67: 2784-2799.
    [12] J. C. Robinson, Infinite-Dimensional Dynamical Systems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2001. doi: 10.1007/978-94-010-0732-0
    [13] Micropolar fluid flows with delay on 2D unbounded domains. J. Appl. Anal. Comput. (2018) 8: 356-378.
    [14] W. Sun, J. Cheng and X. Han, Random attractors for 2D stochastic micropolar fluid flows on unbounded domains, Discrete Contin. Dyn. Syst. Ser. B. doi: 10.3934/dcdsb.2020189
    [15] W. Sun and Y. Li, Asymptotic behavior of pullback attractor for non-autonomous micropolar fluid flows in 2D unbounded domains, Electronic J. Differential Equations, 2018, 21pp.
    [16] Pullback attractor for the 2D micropolar fluid flows with delay on unbounded domains. Bull. Malays. Math. Sci. Soc. (2019) 42: 2807-2833.
    [17] C. Zhao, Pullback asymptotic behavior of solutions for a non-autonomous non-Newtonian fluid on two-dimensional unbounded domains, J. Math. Phys., 53 (2012), 22pp. doi: 10.1063/1.4769302
    [18] Pullback dynamical behaviors of the non-autonomous micropolar fluid flows. Dyn. Partial Differ. Equ. (2015) 12: 265-288.
    [19] $H^1$-uniform attractor and asymptotic smoothing effect of solutions for a nonautonomous micropolar fluid flow in 2D unbounded domains. Nonlinear Anal. Real World Appl. (2008) 9: 608-627.
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