Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant

Abstract The main purpose of this paper is to study the existence of local and global strong solutions for a diffuse-interface model that describes the dynamics of incompressible two-phase viscous flows with surfactant in 3D whole space. We first establish the local existence of strong solutions by using the mollifier technique. Then, applying pure energy method and the standard continuity argument, one proves the global existence of strong solutions provided that initial data is sufficiently small.