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Decay Rates of the Compressible Hall-MHD Equations for Quantum Plasmas

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Abstract

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 \(0 \leq s < \frac{3}{2}\).

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Acknowledgements

X. Xi was supported by Introduction of talent research start-up fund at Guangzhou University, NSF of Guangdong Province (No. 2018A030310312), Colleges Innovation Project of Guangdong (No. 2017KQNCX148), and NSFC (No. 11901127). X. Pu was partially supported by NSFC (No. 11871172) and NSF of Guangdong Province (No. 2019A1515012000). The authors will thank the referees for valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, P.R. China

    Xiaoyu Xi & Xueke Pu

  2. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing, 100088, P.R. China

    Boling Guo

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Xi, X., Pu, X. & Guo, B. Decay Rates of the Compressible Hall-MHD Equations for Quantum Plasmas. Acta Appl Math 170, 459–481 (2020). https://doi.org/10.1007/s10440-020-00342-w

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