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

• 论文 • 上一篇    下一篇

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. 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. 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: 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