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

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  • 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 $t>0$.
    Mathematics Subject Classification: Primary: 35Q30, 76N10; Secondary: 46E35.


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