Low Mach number limit of the non-isentropic ideal magnetohydrodynamic (MHD) equations with large variation of entropy and general initial data in \({\mathbb {R}}^3\) was investigated by Jiang et al. (SIAM J Math Anal 48:302–319, 2016). To obtain the uniform estimates of solutions in \(H^s\) with respect to the Mach number, one of the key assumptions is that the Sobolev index \(s\ge 4\) is even. In this paper, for well-prepared initial data, we revisit the low Mach number limit of the non-isentropic ideal compressible MHD equations with large variation of entropy in the torus \({\mathbb {T}}^3\) and the whole space \({\mathbb {R}}^3\) under lower regularity assumptions by different approaches. First, the uniform estimates of div and curl operators are established by energy methods. Next, by estimating the gradient of vector fields via div and curl operators, we obtain the uniform existence of classical solution on a time interval independent of the Mach number when the initial data are bounded in \(H^3\). Based on the above uniform estimates, the low Mach number limit is established. More precisely, it is rigorously justified that the solution of original equations converges to that of incompressible inhomogeneous MHD equations as the Mach number tends to zero.

Jiang等人研究了具有大熵变化和一般初始数据\({\mathbb {R}}^3\)的非等熵理想磁流体动力学(MHD)方程的低马赫数极限。(SIAM J Math Anal 48:302–319, 2016)。为了获得\(H^s\)中关于马赫数的解的统一估计，关键假设之一是 Sobolev 指数\(s\ge 4\)是偶数。在本文中，对于准备好的初始数据，我们重新审视了非等熵理想可压缩 MHD 方程的低马赫数限制，其中环面\({\mathbb {T}}^3\)和整个空间\({\mathbb {R}}^3\)在通过不同方法的较低规律性假设下。首先，通过能量方法建立div和curl算子的统一估计。接下来，通过div和curl算子估计向量场的梯度，当初始数据以\(H^3\)为界时，我们获得了与马赫数无关的时间间隔上经典解的均匀存在性。基于上述统一估计，建立了马赫数下限。更准确地说，当马赫数趋于零时，原始方程的解收敛到不可压缩非齐次 MHD 方程的解是有严格理由的。