This study investigates the Cauchy problem of an incompressible magnetohydrodynamic system in the rotational framework. Under the assumption that the rotation speed is sufficiently large, the Cauchy problem is shown to be globally well-posed in \(H^{s}({{\mathbb {R}}}^3)\times (L^2\cap L^q) ({{\mathbb {R}}}^3)\) for \(\frac{1}{2}<s < \frac{3}{4}\) and \(3<q < \min \{\frac{6}{3-2s},\,\frac{27}{6 + 4s}\}\).

中文翻译：

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3D不可压缩旋转MHD系统的全球解决方案

这项研究调查了旋转框架中不可压缩的磁流体动力学系统的柯西问题。在旋转速度足够大的假设下，柯西问题在\（H ^ {s}（{{\ mathbb {R}}} ^ 3）\（L ^ 2 \帽L ^ q）（{{\ mathbb {R}}} ^ 3）\）为\（\压裂{1} {2} <S <\压裂{3} {4} \）和\（3 <q <\ min \ {\ frac {6} {3-2s}，\，\ frac {27} {6 + 4s} \} \）。