Navier-Stokes-Cahn-Hilliard system of equations

A growing interest in considering the "hybrid systems " of equations describing more complicated physical phenomena was observed throughout the last 10 years. We mean here, in particular, the so-called Navier-Stokes-Cahn-Hilliard equation, the Navier-Stokes-Poison equations, or the Cahn-Hilliard-Hele-Shaw equation. There are specific difficulties connected with considering such systems. Using the semigroup approach, we discuss here the existence-uniqueness of solutions to the Navier-Stokes-Cahn-Hilliard system, explaining, in particular, the limitation of maximal regularity of the local solutions imposed by the chosen boundary conditions. Published under an exclusive license by AIP Publishing.