Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (5): 1877-1885.doi: 10.1007/s10473-024-0513-4

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THE GLOBAL EXISTENCE AND UNIQUENESS OF SMOOTH SOLUTIONS TO A FLUID-PARTICLE INTERACTION MODEL IN THE FLOWING REGIME*

Lin ZHENG1,†, Shu WANG2   

  1. 1. College of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China;
    2. School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China
  • Received:2023-02-02 Revised:2024-06-11 Online:2024-10-25 Published:2024-10-22
  • Contact: †Lin ZHENG, E-mail,: zhenglin@ncwu.edu.cn
  • About author:Shu WANG,E-mail,: wangshu@bjut.edu.cn
  • Supported by:
    Lin's research was supported by the NSFC (41975129).

Abstract: This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime in R3. Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces, the existence and uniqueness of global smooth solutions in H3 of the system are established by using the careful energy method.

Key words: fluid-particle, flowing regime, global existence

CLC Number: 

  • 35A05
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