Navier–Stokes–Cahn–Hilliard system of equations

Abstract

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.