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On an inhomogeneous boundary value problem for steady compressible magnetohydrodynamics flow

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Abstract

In this paper, we are concerned with the three-dimensional stationary equations of compressible magnetohydrodynamic (MHD) isentropic flow in a bounded cylinder domain \(\Omega =(0,1)\times \Omega _0\) with an inhomogeneous boundary condition. We obtain the existence and uniqueness of a strong solution provided that the data are around a given constant flow. From our result, it reveals that the magnetic Reynolds number plays an important role in the stability of steady compressible MHD equations.

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Acknowledgements

The authors are deeply grateful to the referee for his/her careful reading of the manuscript and very helpful suggestions. The first author was partially supported by the Foundation of Education Department of Liaoning Province (Grant No. LQN201901), Natural Science Foundation of Liaoning Province (Grant No. 2019-MS-152). The second author was supported by the Scientific and Technological Project of Jilin Provinces Education Department in Thirteenth Five-Year (Grant No. JJKH20190180KJ), Natural Science Foundation of Jilin Province (Grant No. 20200201253JC).

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Authors and Affiliations

  1. School of Mathematics, Liaoning University, Shenyang, 110036, Liaoning, People’s Republic of China

    Shengquan Liu

  2. College of Mathematics, Jilin University, Changchun, 130012, Jilin, People’s Republic of China

    Ming Cheng

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  1. Shengquan Liu
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  2. Ming Cheng
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Correspondence to Ming Cheng.

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Liu, S., Cheng, M. On an inhomogeneous boundary value problem for steady compressible magnetohydrodynamics flow. Z. Angew. Math. Phys. 71, 174 (2020). https://doi.org/10.1007/s00033-020-01393-7

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  • DOI: https://doi.org/10.1007/s00033-020-01393-7

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