Mathematical modeling and dissipative structure for systems of magnetohydrodynamics with Hall effect

Abstract

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].