Quasineutral limit of the electro-diffusion model arising in Electrohydrodynamics

The electro-diffusion model, which arises in electrohydrodynamics, is a coupling between the Nernst-Planck-Poisson system and the incompressible Navier-Stokes equations. For the generally smooth doping profile, the quasineutral limit (zero-Debye-length limit) is justified rigorously in Sobolev norm uniformly in time. The proof is based on the elaborate energy analysis and the key point is to establish the uniform estimates with respect to the scaled Debye length.Comment: 20 page

Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations

The full compressible magnetohydrodynamic equations can be derived formally from the complete electromagnetic fluid system in some sense as the dielectric constant tends to zero. This process is usually referred as magnetohydrodynamic approximation in physical books. In this paper we justify this singular limit rigorously in the framework of smooth solutions for well-prepared initial data.Comment: 26page

Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces

The local well-posedness and low Mach number limit are considered for the multi-dimensional isentropic compressible viscous magnetohydrodynamic equations in critical spaces. First the local well-posedness of solution to the viscous magnetohydrodynamic equations with large initial data is established. Then the low Mach number limit is studied for general large data and it is proved that the solution of the compressible magnetohydrodynamic equations converges to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero. Moreover, the convergence rates are obtained.Comment: 37page

Global strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vaccum

This paper considers the initial boundary problem to the planar compressible magnetohydrodynamic equations with large initial data and vacuum. The global existence and uniqueness of large strong solutions are established when the heat conductivity coefficient $\kappa(\theta)$ satisfies \begin{equation*} C_{1}(1+\theta^q)\leq \kappa(\theta)\leq C_2(1+\theta^q) \end{equation*} for some constants $q>0$, and $C_1,C_2>0$.Comment: 19pages,some typos are correcte