We analyze a diffuse interface model that describes the dynamics of incompressible viscous two-phase flows, incorporating mechanisms such as chemotaxis, active transport, and long-range interactions of Oono’s type. The evolution system couples the Navier–Stokes equations for the volume-averaged fluid velocity \(\varvec{v}\) , a convective Cahn–Hilliard equation for the phase-field variable \(\varphi \) , and an advection-diffusion equation for the density of a chemical substance \(\sigma \) . For the initial boundary value problem with a physically relevant singular potential in three dimensions, we demonstrate that every global weak solution \((\varvec{v}, \varphi , \sigma )\) exhibits a propagation of regularity over time. Specifically, after an arbitrary positive time, the phase-field variable \(\varphi \) transitions into a strong solution, whereas the chemical density \(\sigma \) only partially regularizes. Subsequently, the velocity field \(\varvec{v}\) becomes regular after a sufficiently large time, followed by a further regularization of the chemical density \(\sigma \) , which in turn enhances the spatial regularity of \(\varphi \) . Furthermore, we show that every global weak solution stabilizes towards a single equilibrium as \(t\rightarrow +\infty \) . Our analysis uncovers the influence of chemotaxis, active transport, and long-range interactions on the propagation of regularity at different stages of time. The proof relies on several key points, including a novel regularity result for a convective Cahn–Hilliard–diffusion system with a velocity field \(\varvec{v}\) of Leray type, the strict separation property of \(\varphi \) for large times, as well as two conditional uniqueness results pertaining to the full system and its subsystem for \((\varphi , \sigma )\) with a given velocity, respectively.
