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

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.