doi: 10.17706/ijapm.2015.5.1.1-7
Attractors for the Magnetic Bénard Problem
Naoyuki Ishimura
1
,
- 1 Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan
- 2 Nihon University, Kanda-Surugadai, Tokyo 101-8308, Japan.
Abstract
The influence of the magnetic field on the heat convection is an important issue in various industrial productions. The mathematical formulation of such viscous magneto hydrodynamic fluid is given by the magnetic Bénard system. We here show the existence of attractors, which is finite dimensional and characterize the long time dynamics of the system. Furthermore, we estimate their dimensions in terms of the magnetic components as controlling parameters.
Keywords
- Magnetic Bénard system
- attractors
- fractal dimension
How to Cite
Naoyuki Ishimura and Masa Aki Nakamura, "Attractors for the Magnetic Bénard Problem," International Journal of Applied Physics and Mathematics, vol. 5, no. 1, pp. 1-7, 2015. https://doi.org/ 10.17706/ijapm.2015.5.1.1-7
Copyright & License
Copyright © 2015 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).