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

doi:10.1007/s10473-022-0417-0

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (4): 1585-1606.doi: 10.1007/s10473-022-0417-0

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

黄丙远¹, 丁时进², 伍日清³

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

收稿日期:2021-03-02 出版日期:2022-08-25 发布日期:2022-08-23
通讯作者: Shijin DING,E-mail:dingsj@scnu.edu.cn E-mail:dingsj@scnu.edu.cn
基金资助:
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).

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

Bingyuan HUANG¹, Shijin DING², Riqing WU³

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).

摘要/Abstract

摘要： 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.

关键词: Compressibility, fluid-particle system, magnetic field, classical solution

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

中图分类号:

35Q30

黄丙远, 丁时进, 伍日清. CLASSICAL SOLUTIONS OF THE 3D COMPRESSIBLE FLUID-PARTICLE SYSTEM WITH A MAGNETIC FIELD[J]. 数学物理学报(英文版), 2022, 42(4): 1585-1606.

Bingyuan HUANG, Shijin DING, Riqing WU. CLASSICAL SOLUTIONS OF THE 3D COMPRESSIBLE FLUID-PARTICLE SYSTEM WITH A MAGNETIC FIELD[J]. Acta mathematica scientia,Series B, 2022, 42(4): 1585-1606.

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

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

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