zbMATH — the first resource for mathematics

Global attractor for heat convection problem in a micropolar fluid. (English) Zbl 1191.37042
The author uses the model proposed by Eringen, which is the generalization of the Navier-Stokes model. The behaviour of the fluid layer filling the region between two rigid surfaces is studied. The existence and the uniqueness of global in time solutions and existence of global attractor is shown. The Hausdorff dimension of the global attractor is estimated.

37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
35B41 Attractors
35Q35 PDEs in connection with fluid mechanics
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76D05 Navier-Stokes equations for incompressible viscous fluids
76R05 Forced convection
PDF BibTeX Cite
Full Text: DOI
[1] Eringen, Journal of Mathematical Mechanics 16 pp 1– (1996)
[2] Popel, Biorheology 11 pp 427– (1974)
[3] . Hydrodynamics and Heat Exchange for Gradient Flows of Fluid with Micro- structure. Nauka i Technika: Minsk, 1984 (in Russian).
[4] Forste, Advances in Mechanics 2 pp 81– (1979)
[5] Yamaguchi, Mathematical Methods in the Applied Mathematics 28 pp 1507– (2005)
[6] Łukaszewicz, Mathematical and Computer Modelling 34 pp 487– (2001)
[7] Foias, Nonlinear Analysis, TMA 11 pp 939– (1987)
[8] Cross, Physical Review A 27 pp 229– (1983)
[9] Koschmieder, Advances in Chemical Physics 26 pp 177– (1974)
[10] Busse, Reports on Progress in Physics 41 pp 1929– (1978)
[11] Getling, Soviet Physics–Uspekhi 34 pp 737– (1991)
[12] Rayleigh–Benard Convection: Structures and Dynamics. World Scientific: Singapore, 1998.
[13] Siddheshwar, International Journal of Applied Mechanics and Engineering 7 pp 513–
[14] Sharma, Czechoslovak Journal of Physics 50 pp 1133– (2000)
[15] Sherif, International Journal of Engineering Science 36 pp 1183– (1998)
[16] Birnir, Journal of Nonlinear Mathematical Physics 7 pp 136– (2000)
[17] Doering, Physica D 123 pp 206– (1998)
[18] Navier–Stokes Equations and Nonlinear Functional Analysis. Society for Industrial and Applied Mathematics: Philadelphia, PA, 1983. · JFM 07.0137.01
[19] Lectures on Elliptic Boundary Value Problems. Elsevier: New York, 1965.
[20] Partial Differential Equations. American Mathematical Society: Providence, RI, 1998.
[21] Infinite Dimensional Dynamical Systems in Mechanics and Physics. Springer: New York, 1997.
[22] Boukrouche, Mathematical Methods in the Applied Sciences 28 pp 1673– (2005)
[23] Navier–Stokes Equations. Theory and Numerical Analysis. Society for Industrial and Applied Mathematics: Philadelphia, PA, 1983.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.