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Remarks on classical solutions to steady quantum Navier-Stokes equations

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Abstract

The paper of Dong [Dong, J. Classical solutions to one-dimensional stationary quantum Navier–Stokes equations, J. Math Pure Appl. 2011] which proved the existence of classical solutions to one-dimensional steady quantum Navier–Stokes equations, when the nonzero boundary value u 0 satisfies some conditions. In this paper, we obtain a different version of existence theorem without restriction to u 0. As a byproduct, we get the existence result of classical solutions to the stationary quantum Navier–Stokes equations.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Mohamed Ahmed Abdallah

  2. Mathematics School & Institute, Jilin University, Changchun, 130012, China

    Xu-yang Sun

  3. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Wei-wei Wang

  4. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Jun-ping Yin

Authors
  1. Mohamed Ahmed Abdallah
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  2. Xu-yang Sun
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  3. Wei-wei Wang
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  4. Jun-ping Yin
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Corresponding author

Correspondence to Jun-ping Yin.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. U1430103).

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Abdallah, M.A., Sun, Xy., Wang, Ww. et al. Remarks on classical solutions to steady quantum Navier-Stokes equations. Acta Math. Appl. Sin. Engl. Ser. 32, 957–962 (2016). https://doi.org/10.1007/s10255-016-0616-3

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  • DOI: https://doi.org/10.1007/s10255-016-0616-3

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