Mathematical study of multi‐phase flow under shear through order parameter formulation

Source abstract

In this paper we study the coupling of the Navier–Stokes equations and the Cahn–Hilliard equation which stands for a model of a multi‐phase fluid under shear. We first study existence and uniqueness of solutions of the system in dimension $2$ and $3$ even if the diffusion coefficient is allowed to degenerate. In the last part, an asymptotic stability result is shown.