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Global Existence and Decay Estimates for the Classical Solutions to a Compressible Fluid-Particle Interaction Model

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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.

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Authors and Affiliations

  1. South China Research Center for Applied Mathematics and Interdisciplinary Studies, School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Shijin Ding

  2. School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China

    Bingyuan Huang

  3. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

    Quanrong Li

Authors
  1. Shijin Ding
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  2. Bingyuan Huang
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  3. Quanrong Li
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Corresponding author

Correspondence to Bingyuan Huang.

Additional information

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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Ding, S., Huang, B. & Li, Q. Global Existence and Decay Estimates for the Classical Solutions to a Compressible Fluid-Particle Interaction Model. Acta Math Sci 39, 1525–1537 (2019). https://doi.org/10.1007/s10473-019-0605-8

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

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