# American Institute of Mathematical Sciences

December  2016, 9(6): 1717-1752. doi: 10.3934/dcdss.2016072

## Local classical solutions of compressible Navier-Stokes-Smoluchowski equations with vacuum

 1 School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China 2 Department of Mathematics, South China Normal University, Guangzhou, Guangdong 510631 3 School of Mathematics, South China University of Technology, Guangzhou 510641, China

Received  July 2015 Revised  September 2016 Published  November 2016

This paper is concerned with the Cauchy problem for compressible Navier-Stokes-Smoluchowski equations with vacuum in $\mathbb{R}^3$. We prove both existence and uniqueness of the local strong solution, and then obtain a local classical solution by deriving the smoothing effect of the strong solution for $t>0$.
Citation: Bingyuan Huang, Shijin Ding, Huanyao Wen. Local classical solutions of compressible Navier-Stokes-Smoluchowski equations with vacuum. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1717-1752. doi: 10.3934/dcdss.2016072
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