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 H3(ℝ3)∩L1(ℝ3)$$ {H}^3\left({\mathbb{R}}^3\right)\cap {L}^1\left({\mathbb{R}}^3\right) $$, we prove that the strong solution converges to the equilibrium state at an optimal algebraic rate (1+t)−3/4$$ {\left(1+t\right)}^{-3/4} $$ in L2$$ {L}^2 $$‐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$$ {\left(1+t\right)}^{-5/4} $$ in L2$$ {L}^2 $$‐norm. [ABSTRACT FROM AUTHOR]