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Low Mach number limit of compressible two-fluid model

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Abstract

In this paper, we consider the low Mach number limit of the weak solutions to the viscous compressible two-fluid model with one velocity and a pressure of two components in three spatial dimensions. For well-prepared initial data, we prove rigorously that the weak solutions of the compressible two-fluid model converge to the strong solution of the incompressible Navier–Stokes equations as the Mach number tends to zero. Here, we allow that the two densities converge to different limits. Furthermore, the rates of convergence are also obtained.

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Acknowledgements

J. Yang’s research was partially supported by the Joint Funds of the National Natural Science Foundation of China (Grant No. U1204103).

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Authors and Affiliations

  1. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, 450045, Henan Province, People’s Republic of China

    Jianwei Yang & Peng Cheng

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  1. Jianwei Yang
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  2. Peng Cheng
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Correspondence to Jianwei Yang.

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Yang, J., Cheng, P. Low Mach number limit of compressible two-fluid model. Z. Angew. Math. Phys. 71, 9 (2020). https://doi.org/10.1007/s00033-019-1233-9

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  • DOI: https://doi.org/10.1007/s00033-019-1233-9

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