Incompressible limit of the compressible non-isentropic   magnetohydrodynamic equations with zero magnetic diffusivity
  We study the incompressible limit of the compressible non-isentropic magnetohydrodynamic equations with zero magnetic diffusivity and general initial data in the whole space $\mathbb{R}^d$ $(d=2,3)$. We first establish the existence of classic solutions on a time interval independent of the Mach number. Then, by deriving uniform a priori estimates, we obtain the convergence of the solution to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero. 
Song Jiang, Qiangchang Ju, and Fucai Li
math.AP