Global well-posedness and long time behavior of strong solutions for a fluid–particle interaction model in three dimensions

In this paper, we consider Cauchy problem for a compressible fluid-particle interaction system in three dimensions. Under some assumptions that the initial data are of a small perturbation around a nontrivial stationary profile in H2(R3) norm, we obtain the global existence and uniqueness of the solutions. Long-time behavior of the solution is also studied. More specifically, based on the analysis of Green’s matrix for the linearized system and the classification of the nonlinear terms on different decays in time, we obtain Lp-norm estimates of the solutions.