This paper is concerned with the mathematical modeling of electro-magneto-hydrodynamics and magnetohydrodynamics by taking account of the Hall effect. We discuss conservation laws, strict convexity of the negative entropy as a function of conserved quantities, and the associated energy form. Moreover, we investigate the dissipative structure and decay properties of the linearized systems as applications of the general theory developed in Umeda et al. [On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics, Japan J. Appl. Math. 1 (1984) 435–457] and Shizuta and Kawashima [Systems of equations of hyperbolic–parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985) 249–275].

本文关注的是考虑霍尔效应的电磁流体动力学和磁流体动力学的数学建模。我们讨论守恒定律、作为守恒量函数的负熵的严格凸性以及相关的能量形式。此外，我们研究了线性化系统的耗散结构和衰减特性，作为 Umeda等人开发的一般理论的应用。[关于电磁流体动力学线性化方程的解的衰减，日本 J. Appl。数学。 1 (1984) 435–457] 和 Shizuta 和 Kawashima [应用于离散玻尔兹曼方程的双曲抛物型方程组，北海道数学。J.  14(1985) 249–275]。