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

Shijin DING; Bingyuan HUANG; Quanrong LI

doi:10.1007/s10473-019-0605-8

Acta mathematica scientia, Series B >

2019 , Vol. 39 >Issue 6: 1525 - 1537

DOI: https://doi.org/10.1007/s10473-019-0605-8

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

Shijin DING ,
Bingyuan HUANG ,
Quanrong LI

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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 date: 2018-08-30

Revised date: 2019-05-09

Online published: 2019-12-30

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).

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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

Cite this article

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 . DOI: 10.1007/s10473-019-0605-8

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