Global well-posedness of classical solutions to a fluid-particle interaction model in R3

We consider the Cauchy problem of a fluid-particle interaction model in R3, namely, compressible Navier-Stokes equations coupled with Smoluchowski equation. When the initial data (ρ0,u0,η0) is of small energy around steady state (ρ⋆,0,η⋆), the global well-posedness and large-time behavior of classical solutions are investigated. Vacuum is allowed.