Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (4): 1585-1606.doi: 10.1007/s10473-022-0417-0

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CLASSICAL SOLUTIONS OF THE 3D COMPRESSIBLE FLUID-PARTICLE SYSTEM WITH A MAGNETIC FIELD

Bingyuan HUANG1, Shijin DING2, Riqing WU3   

  1. 1. School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China;
    2. South China Research Center for Applied Mathematics and Interdisciplinary Studies, School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China;
    3. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China
  • Received:2021-03-02 Online:2022-08-25 Published:2022-08-23
  • Contact: Shijin DING,E-mail:dingsj@scnu.edu.cn E-mail:dingsj@scnu.edu.cn
  • Supported by:
    The first author was supported by the National Natural Science Foundation of China (12026253, 12026244, 11971357), the Natural Science Foundation of Guangdong Province (2018A030310008, 2021A1515010303), Guangdong Key Laboratory for Functional Substances in Medicinal Edible Resources and Healthcare Products (2021B1212040015), NSF of Guangdong Provincial Department of Education (2019KTSCX097), and Chaozhou Science and Technology plan project (2019ZC02). The second author was supported by the Key Project of National Natural Science Foundation of China (12131010), the National Natural Science Foundation of China (11771155, 11571117, 11871005), the Natural Science Foundation of Guangdong Province (2017A030313003, 2019A1515011491, 2021A1515010249), and the Science and Technology Program of Guangzhou (2019050001).

Abstract: This paper addresses the 3-D Cauchy problem of a fluid-particle system with a magnetic field. First, the local classical solutions of the linearized model on the sphere $B_{r} $ are obtained by some a priori estimates that do not depend on the radius $r$. Second, the classical solutions of the linearized model in $\mathbb{R}^{3}$ are obtained by combining the continuation and compactness methods. Finally, the classical solutions of the original system are proved by use of the picard iteration argument and the energy method.

Key words: Compressibility, fluid-particle system, magnetic field, classical solution

CLC Number: 

  • 35Q30
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