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## Magnetohydrodynamic equations

In his paper titled On the magnetic Bénard problem M.-A. Nakamura in 1991 (J. Fac. Sci. Univ. Tokyo Sect. IA Math., 38, 359-393) derivated the following problem:
where the variables  and  denote the velocity vector, the magnetic field and the pressure, repsectively. The constants  and  represent the unit mass density, the magnetic permeability, the electric conductivity and the kinematic viscosity, respectively. As usual  gives the outer force to the fluid. In recent research uniqueness results are obtained under the following growth and boundedness conditions:
Meanwhile several examples for non-uniquness are known. Under some conditions an iteration process could be found for the corresponding stationary problem (cf. W. Sprößig, Quaternionic Analysis in Fluid Mechanics (2000) In: J. Ryan/W. Sprößig: Clifford Algebras and their applications in Mathematical Physics, Volume 2, Clifford Analysis, Birkhäuser, Progress in Physics, 37-54.)

A late reference: N. Ishimura and Nakamura M. (1997) Uniqueness for Unbounded Classical Solutions of the MHD Equations, MMAS, 20 617-623.

collected and worked out by Wolfgang Sprößig, TU-Bergakademie Freiberg