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We analyze a Navier-Stokes-Cahn-Hilliard model for viscous incompressibletwo-phase flows where the mechanisms of chemotaxis, active transport andreaction are taken into account. The evolution system couples the Navier-Stokesequations for the volume-averaged fluid velocity, a convective Cahn-Hilliardequation for the phase-field variable, and an advection-diffusion equation forthe density of certain chemical substance. This system is thermodynamicallyconsistent and generalizes the well-known ``Model H'' for viscousincompressible binary fluids. For the initial-boundary value problem with aphysically relevant singular potential in a general bounded smooth domain$\Omega\subset \mathbb{R}^3$, we first prove the existence and uniqueness of alocal strong solution. When the initial velocity is small and the initialphase-field function as well as the initial chemical density are smallperturbations of a local minimizer of the free energy, we establish theexistence of a unique global strong solution. Afterwards, we show theuniqueness of asymptotic limit for any global strong solution as time goes toinfinity and provide an estimate on the convergence rate. The proofs for globalwell-posedness and long-time behavior are based on the dissipative structure ofthe system and the Lojasiewicz-Simon approach. Our analysis reveals the effectsof chemotaxis, active transport and a long-range interaction of Oono's type onthe global dynamics of the coupled system.

On a Navier-Stokes-Cahn-Hilliard System for Viscous Incompressible Two-phase Flows with Chemotaxis, Active Transport and Reaction