Strong solutions to a fluid-particle interaction model with magnetic field in $ \mathbb{R}^2 $

Shijin Ding; Bingyuan Huang; Xiaoyan Hou

doi:10.3934/dcdsb.2021042

Article Contents

2022, Volume 27, Issue 1: 277-300. Doi: 10.3934/dcdsb.2021042

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Strong solutions to a fluid-particle interaction model with magnetic field in $ \mathbb{R}^2 $

1.
South China Research Center for Applied Mathematics and Interdisciplinary Studies and School of Mathematical Sciences, South China Normal University Guangzhou, 510631, China
2.
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China
3.
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

^* Corresponding author: Bingyuan Huang
^* Corresponding author: Bingyuan Huang

Received: November 30, 2019

Early access: January 2021

Published: January 2022

The first author is supported by the National Natural Science Foundation of China (Nos. 11371152, 11771155, 11571117, 11871005), the Natural Science Foundation of Guangdong Province (Nos. 2017A030313003, 2019A1515011491), and the Science and Technology Program of Guangzhou (No. 2019050001). The second author is supported by the National Natural Science Foundation of China(Nos. 12026253, 12026244, 11971357), and the Natural Science Foundation of Guangdong Province (No. 2018A030310008)

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Abstract

A fluid-particle interaction model with magnetic field is studied in this paper. When the initial vacuum and the far field vacuum of the fluid and the particles are contained, the constant shear viscosity $ \mu $ and the bulk viscosity $ \lambda $ are $ \mu>0 $ $ \lambda = \rho^\beta $ for any $ \beta\geq 0 $, the strong solutions of the 2D Cauchy problem for the coupled system are established applying the method of weighted estimates in Li-Liang's paper on Navier-Stokes equations.

Keywords:

Compressible Navier-Stokes-Smoluchowski equations,
magnetic field,
strong solution,
vacuum.

Mathematics Subject Classification: Primary: 35Q30, 76N10; Secondary: 46E35.

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References

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