GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE CLASSICAL SOLUTIONS TO A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL

doi:10.1007/s10473-019-0605-8

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (6): 1525-1537.doi: 10.1007/s10473-019-0605-8

GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE CLASSICAL SOLUTIONS TO A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL

丁时进¹, 黄丙远², 黎泉荣³

1. South China Research Center for Applied Mathematics and Interdisciplinary Studies, School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
2. School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China;
3. College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China

收稿日期:2018-08-30 修回日期:2019-05-09 出版日期:2019-12-25 发布日期:2019-12-30
通讯作者: Bingyuan HUANG,E-mail:huangby04@126.com E-mail:huangby04@126.com
作者简介:Shijin DING,E-mail:dingsj@scnu.edu.cn;Quanrong LI,E-mail:787177237@qq.com
基金资助:
Ding was supported by the National Natural Science Foundation of China (11371152, 11771155, 11571117 and 11871005), and by the Natural Science Foundation of Guangdong Province (2017A030313003). Huang was supported by the Natural Science Foundation of Guangdong Province (2018A030310008), and by the Doctoral Scientific Research Foundation of Hanshan Normal University (QD20171002) and the Educational Commission of Guangdong Province (2017KTSCX124).

GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE CLASSICAL SOLUTIONS TO A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL

Shijin DING¹, Bingyuan HUANG², Quanrong LI³

1. South China Research Center for Applied Mathematics and Interdisciplinary Studies, School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
2. School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China;
3. College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China

Received:2018-08-30 Revised:2019-05-09 Online:2019-12-25 Published:2019-12-30
Contact: Bingyuan HUANG,E-mail:huangby04@126.com E-mail:huangby04@126.com
Supported by:
Ding was supported by the National Natural Science Foundation of China (11371152, 11771155, 11571117 and 11871005), and by the Natural Science Foundation of Guangdong Province (2017A030313003). Huang was supported by the Natural Science Foundation of Guangdong Province (2018A030310008), and by the Doctoral Scientific Research Foundation of Hanshan Normal University (QD20171002) and the Educational Commission of Guangdong Province (2017KTSCX124).

摘要/Abstract

摘要： We prove the global existence of classical solutions to a fluid-particle interaction model in R³, namely, compressible Navier-Stokes-Smoluchowski equations, when the initial data are close to the stationary state (ρ_⋆, 0, η_⋆) and the external potential satisfies the smallness assumption. Furthermore, optimal decay rates of classical solutions in H³-framework are obtained.

关键词: compressible Navier-Stokes-Smoluchowski, global classical solutions, optimal decay rates

Abstract: We prove the global existence of classical solutions to a fluid-particle interaction model in R³, namely, compressible Navier-Stokes-Smoluchowski equations, when the initial data are close to the stationary state (ρ_⋆, 0, η_⋆) and the external potential satisfies the smallness assumption. Furthermore, optimal decay rates of classical solutions in H³-framework are obtained.

Key words: compressible Navier-Stokes-Smoluchowski, global classical solutions, optimal decay rates

中图分类号:

35Q30

丁时进, 黄丙远, 黎泉荣. GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE CLASSICAL SOLUTIONS TO A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL[J]. 数学物理学报(英文版), 2019, 39(6): 1525-1537.

Shijin DING, Bingyuan HUANG, Quanrong LI. GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE CLASSICAL SOLUTIONS TO A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL[J]. Acta mathematica scientia,Series B, 2019, 39(6): 1525-1537.

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GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE CLASSICAL SOLUTIONS TO A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL

GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE CLASSICAL SOLUTIONS TO A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL

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