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This paper studies the convergence of the compressible isentropic magnetohydrodynamic equations to the corresponding incompressiblemagnetohydrodynamic equations with *ill-prepared*initial data in a periodic domain.We prove that the solution to the compressible isentropic magnetohydrodynamic equations with small Mach number exists uniformly in the time interval as long as that to the incompressible one does. Furthermore,we obtain the convergence result for the solutions filtered by the group of acoustics.

In this paper we study the low Mach number limit of the full compressible Hall-magnetohydrodynamic (Hall-MHD) system in $\mathbb{T}^3$. We prove that, as the Mach number tends to zero, the strong solution of the full compressible Hall-MHD system converges to that of the incompressible Hall-MHD system.

$κ(θ)$ |

$C_{1}(1+\theta^q)\leq \kappa(\theta)\leq C_2(1+\theta^q)$ |

$q>0$ |

$C_1,C_2>0$ |

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.

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