Mathematical study of multiphase flow under shear through order parameter formulation
Résumé
In this paper we study the coupling of the Navier-Stokes equations and the Cahn-Hilliard equation which stands for a model of a multiphase 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.