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.

Index Terms—Magnetic Bénard system, attractors, fractal dimension.

Naoyuki Ishimura is with Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan (email: ishimura@econ.hit-u.ac.jp).
Masa Aki Nakamura is with Nihon University, Kanda-Surugadai, Tokyo 101-8308, Japan.

Cite: Naoyuki Ishimura, Masa Aki Nakamura, "Attractors for the Magnetic Bénard Problem," International Journal of Applied Physics and Mathematics vol. 5, no. 1, pp. 1-7, 2015.