We consider the Cauchy problem to the 1D non-resistive compressible magnetohydrodynamics (MHD) equations. We establish the global existence and uniqueness of strong solutions for large initial data and vacuum when the viscosity coefficient is assumed to be constant or density-dependent. The analysis is based on the full use of effective viscous flux and the Caffarelli–Kohn–Nirenberg weighted inequality to get the higher-order estimates of the solutions. This result could be viewed as the first one on the global well-posedness of strong solutions to the Cauchy problem of 1D non-resistive compressible MHD equations while the initial data may be arbitrarily large and permit vacuum.

中文翻译：

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无电阻率的一维可压缩MHD方程Cauchy问题的全局强解

我们将柯西问题考虑到一维非电阻可压缩磁流体动力学（MHD）方程中。当粘度系数被假定为常数或依赖于密度时，我们建立了针对大量初始数据和真空的强解的整体存在性和唯一性。该分析基于充分利用有效粘性通量和Caffarelli-Kohn-Nirenberg加权不等式来获得解的高阶估计。这一结果可以看作是关于一维非电阻可压缩MHD方程Cauchy问题的强解的整体适定性的第一个结果，而初始数据可能任意大，并允许真空。