Global well-posedness of a Navier-Stokes-Cahn-Hilliard system with chemotaxis and singular potential in 2D (Q2042671)

The authors study the evolution problem for a thermodynamically consistent model derived in [\textit{K. F. Lam} and \textit{H. Wu}, Eur. J. Appl. Math. 29, No. 4, 595--644 (2018; Zbl 1397.92100)] a two-phase incompressible fluid mixture, based on the Cahn-Hilliard equation coupled with the Navier-Stokes equations, that includes chemotactic effects. Existence of strong solutions is proved in the two-dimensional setting, and some properties (such as separation from pure states) of them are shown.