Applications of Mathematics, first online, pp. 1-18


Incompressible limit of a fluid-particle interaction model

Hongli Wang, Jianwei Yang

Received September 30, 2019.   Published online November 27, 2020.

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.
Keywords:  incompressible limit; relative entropy method; fluid-particle interaction model; incompressible Navier-Stokes equation
Classification MSC:  35B25, 35G25, 35Q35
DOI:  10.21136/AM.2020.0253-19

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Affiliations:   Hongli Wang, School of Physics and Electronics, North China University of Water Resources and Electric Power, Zhengzhou 450045, Henan Province, P. R. China, e-mail: wanghongli@ncwu.edu.cn, Jianwei Yang (corresponding author), School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450045, Henan Province, P. R. China, yangjianwei@ncwu.edu.cn


 
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