In this paper, decay rates of the compressible Hall-MHD equations for quantum plasmas in three-dimensional whole space are studied. By using a general energy method, the time decay rates for higher-order spatial derivatives of density, velocity and magnetic field are established when the initial perturbation belongs to \(\dot{H}^{-s}\) with \(0 \leq s < \frac{3}{2}\).

中文翻译：

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量子等离子体的可压缩Hall-MHD方程的衰减率

本文研究了三维整体空间中等离子的可压缩Hall-MHD方程的衰减率。通过使用一般能量方法，当初始扰动属于\（\ dot {H} ^ {-s} \）为\（0 ）时，建立了密度，速度和磁场的高阶空间导数的时间衰减率。\ leq s <\ frac {3} {2} \）。