This paper is concerned with the low Mach number limit of the compressible Hall-magnetohydrodynamic model for quantum plasmas in \( {\mathbb {T}}^{3}\). It is justified rigorously that, for the well-prepared initial data, as the Mach number tends to zero, the classical solution of the compressible quantum Hall-magnetohydrodynamic model converges to that of the incompressible Hall-magnetohydrodynamic model.

中文翻译：

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具有量子效应的可压缩霍尔磁流体力学模型的渐近极限

本文关注\（{\\ mathbb {T}} ^ {3} \）中量子等离子体的可压缩霍尔磁流体力学模型的低马赫数极限。严格证明，对于良好准备的初始数据，随着马赫数趋于零，可压缩量子霍尔磁流体力学模型的经典解收敛于不可压缩霍尔磁流体力学模型的经典解。