Optimal decay rate of solutions to the two-phase flow model

This article is devoted to the study of the global existence and large time behavior of the three-dimensional two-phase flow model derived from the Chapman-Enskog expansion of the Navier-Stokes-Vlasov-Fokker-Planck equations around the local Maxwellian. When the initial data are a small perturbation of the equilibrium state in H-3(R-3) boolean AND L-1 (R-3), we prove that the strong solution converges to the equilibrium state at an optimal algebraic rate (1+t)(-3/4) in L-2-norm. It is observed that due to the dispersion effect of the drag force term, the difference of velocities decays at a faster rate (1+t)(-5/4) in L-2-norm.