zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

35B41Attractors (PDE)
35Q30Stokes and Navier-Stokes equations
Full Text: DOI
[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) · Zbl 1020.76003
[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) · Zbl 1026.37500
[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) · Zbl 0871.35001