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Pullback attractor for heat convection problem in a micropolar fluid. (English) Zbl 1189.35030
Summary: We consider a two-dimensional micropolar fluid flow heated from below. We assume that the temperature of the lower part of the boundary is a function of time. That leads to the non-autonomous system of equations. We show the existence of the pullback attractor for the problem. Next, the dimension of the attractor is estimated from above.
MSC:
 35B41 Attractors (PDE) 35Q30 Stokes and Navier-Stokes equations
References:
 [1] Temam, R.: Navier–Stokes equations and nonlinear functional analysis, (1983) · Zbl 0522.35002 [2] łukaszewicz, G.: Long time behavior of 2D micropolar fluid flows, Mathematical and computer modelling 34, 487-509 (2001) [3] Tarasińska, A.: Global attractor for heat convection problem in a micropolar fluid, Mathematical methods in applied sciences 29, No. 11, 1215-1236 (2006) · Zbl 1191.37042 · doi:10.1002/mma.720 [4] Caraballo, T.; łukaszewicz, G.; Real, J.: Pullback attractors for non-autonomous 2D Navier–Stokes equations in some unbounded domains, Comptes rendus mathematique 342, No. 4, 263-268 (2006) · Zbl 1085.37054 · doi:10.1016/j.crma.2005.12.015 [5] Robinson, J. C.: Infinite dimensional systems, (2001) [6] Boukrouche, M.; łukaszewicz, G.: Attractor dimension estimate for plane shear flow of micropolar fluid with free boundary, Mathematical methods in the applied sciences 28, 1673-1694 (2005) · Zbl 1081.35071 · doi:10.1002/mma.630 [7] Cheban, D. N.; Kloeden, P. E.; Schmalfuss, B.: The relationship between pullback, forward and global attractors of nonautonomous dynamical systems, Nonlinear dynamics and systems theory 2, 9-28 (2002) · Zbl 1054.34087 [8] Caraballo, T.; łukaszewicz, G.; Real, J.: Pullback attractors for asymptotically compact nonautonomous dynamical systems, Nonlinear analysis TMA 64, 484-498 (2006) · Zbl 1128.37019 · doi:10.1016/j.na.2005.03.111 [9] łukaszewicz, G.; Sadowski, W.: Uniform attractor for 2D magnetomicropolar fluid flow in some unbounded domains, Zeitschrift für angewandte Mathematik und physik 55, 1-11 (2004) [10] Rosa, R.: The global attractor for the 2D Navier–Stokes flow on some unbounded domains, Nonlinear analysis TMA 32, No. 1, 71-85 (1998) · Zbl 0901.35070 · doi:10.1016/S0362-546X(97)00453-7 [11] Moise, I.; Rosa, R.; Wang, X.: Attractors for noncompact nonautonomous systems via energy equations, Discrete and continuous dynamical systems 10, 473-496 (2004) · Zbl 1060.35023 · doi:10.3934/dcds.2004.10.473 [12] Eringen, A. C.: Theory of micropolar fluids, Journal of mathematical mechanics 16, No. 1, 1-16 (1996) [13] Constantin, P.; Foias, C.; Temam, R.: Attractors representing turbulent flows, Memories of the American mathematical society 53 (1984) [14] Foias, C.; Manley, O.; Temam, R.: Attractors for the Bénard problem: existence and physical bounds on their fractal dimension, Nonlinear analysis TMA 11, No. 8, 939-967 (1987) · Zbl 0646.76098 · doi:10.1016/0362-546X(87)90061-7 [15] Langa, J. A.; łukaszewicz, G.; Real, J.: Finite fractal dimension of pullback attractor for non-autonomous 2-D Navier–Stokes in some unbounded domains, Nonlinear analysis TMA 66, 735-749 (2007) · Zbl 1113.37055 · doi:10.1016/j.na.2005.12.017 [16] Temam, R.: Infinite dimensional dynamical systems in mechanics and physics, (1997)