This paper considers the problem of the local existence for the generalized MHD equations with fractional dissipative terms \(\Lambda ^{2\alpha } u\) for the velocity field and \(\Lambda ^{2\beta } b\) for the magnetic field, respectively. Based on some new commutator estimates, local existence for the generalized MHD equations is established, which recovers and improves previous results.

中文翻译：

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广义MHD方程的带分数导数和局部存在的交换子估计。

本文考虑的局部存在性对于具有分数耗散项广义MHD方程的问题（\ LAMBDA ^ {2 \阿尔法} U \）\为速度场和\（\ LAMBDA ^ {2 \的β} b \）为磁场。基于一些新的换向器估计，建立了广义MHD方程的局部存在性，从而恢复并改善了先前的结果。