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Incompressible Limit of a Fluid-Particle Interaction Model

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Abstract

The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes to zero. Furthermore, the desired convergence rates are also obtained.

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Authors and Affiliations

  1. School of Physics and Electronics, North China University of Water Resources and Electric Power, Zhengzhou, Henan Province, 450045, P. R. China

    Hongli Wang

  2. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, Henan Province, 450045, P. R. China

    Jianwei Yang

Authors
  1. Hongli Wang
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  2. Jianwei Yang
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Correspondence to Jianwei Yang.

Additional information

This work was partially supported by National Natural Science Foundation of China (No. 12061040).

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Wang, H., Yang, J. Incompressible Limit of a Fluid-Particle Interaction Model. Appl Math 66, 69–86 (2021). https://doi.org/10.21136/AM.2020.0253-19

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