Global well-posedness of classical solutions to a fluid–particle interaction model in [formula omitted

Abstract

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.