In this paper, we first provide a derivation of compressible nonisentropic Hall-magnetohydrodynamic (Hall-MHD) system from generalized Ohm's law. Then, we prove the global existence of strong solutions for the compressible nonisentropic Hall-MHD model based on the standard energy method in -framework. Finally, optimal decay rates of strong solutions in -norm are obtained if the initial data belong to additionally.

In this paper, we consider two incompressible nematic type liquid crystal models in threedimensional space. Blow-up criterions for weak and smooth solutions are established in homogenous and nonhomogenous Besov space with negative regular index, respectively. As a result, we improve some previous results in Besov space.

In this study, we consider the initial boundary value problem of the planar magnetohydrodynamics (MHD) system when the viscous coefficients and heat conductivity depend on the temperature, which are assumed to be proportional to θ α , α ≥ 0 , and θ β , β ≥ 0 , respectively, and magnetic diffusivity coefficient depends on the specific volume. We prove the existence and uniqueness of the global-in-time classical solution with general large initial data provided that α is sufficiently small and there is no restriction on the parameter β . Moreover, the nonlinearly exponential stability of the solution is obtained. As a result, we extend the works given by Sun et al. for the full compressible Navier-Stokes equations and by Li and Shang for the full compressible MHD equations.