Incompressible limit of the non-isentropic ideal magnetohydrodynamic equations

Abstract

We study the incompressible limit of the compressible non-isentropic ideal magnetohydrodynamic equations with 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.