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Long-time behavior of solutions for the compressible quantum magnetohydrodynamic model in \({\mathbb {R}}^3\)

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Abstract

In this paper, long-time behavior of solutions for the compressible viscous quantum magnetohydrodynamic model in three-dimensional whole space is studied. We establish the optimal time decay rates for higher-order spatial derivatives of density, velocity and magnetic field, which improve the work of Pu and Xu (Z Angew Math Phys 68:18, 2017).

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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) and the project for young creative talents of Higher Education of Guangdong Province (No. 2017KQNCX148). X. Pu was supported by NSFC (No. 11471057). B. Guo was partially supported by NSFC (No. 11731014). The authors 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, People’s Republic of China

    Xiaoyu Xi & Xueke Pu

  2. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009,  Beijing, 100088, People’s Republic of China

    Boling Guo

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  1. Xiaoyu Xi
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  2. Xueke Pu
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  3. Boling Guo
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Correspondence to Xiaoyu Xi.

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Xi, X., Pu, X. & Guo, B. Long-time behavior of solutions for the compressible quantum magnetohydrodynamic model in \({\mathbb {R}}^3\). Z. Angew. Math. Phys. 70, 7 (2019). https://doi.org/10.1007/s00033-018-1049-z

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  • DOI: https://doi.org/10.1007/s00033-018-1049-z

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