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

doi:10.1007/s10473-024-0513-4

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (5): 1877-1885.doi: 10.1007/s10473-024-0513-4

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

Lin ZHENG^1,†, Shu WANG²

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

收稿日期:2023-02-02 修回日期:2024-06-11 出版日期:2024-10-25 发布日期:2024-10-22
通讯作者: †Lin ZHENG, E-mail,: zhenglin@ncwu.edu.cn
作者简介:Shu WANG,E-mail,: wangshu@bjut.edu.cn
基金资助:
Lin's research was supported by the NSFC (41975129).

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

Lin ZHENG^1,†, Shu WANG²

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).

摘要/Abstract

摘要： This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime in $\mathbb{R}^{3}$. 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 $H^{3}$ of the system are established by using the careful energy method.

关键词: fluid-particle, flowing regime, global existence

Abstract: This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime in $\mathbb{R}^{3}$. 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 $H^{3}$ of the system are established by using the careful energy method.

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

中图分类号:

35A05

Lin ZHENG, Shu WANG. THE GLOBAL EXISTENCE AND UNIQUENESS OF SMOOTH SOLUTIONS TO A FLUID-PARTICLE INTERACTION MODEL IN THE FLOWING REGIME^*[J]. 数学物理学报(英文版), 2024, 44(5): 1877-1885.

Lin ZHENG, Shu WANG. THE GLOBAL EXISTENCE AND UNIQUENESS OF SMOOTH SOLUTIONS TO A FLUID-PARTICLE INTERACTION MODEL IN THE FLOWING REGIME^*[J]. Acta mathematica scientia,Series B, 2024, 44(5): 1877-1885.

参考文献

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

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

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