On Non-Newtonian fluids and phase field approach: Existence and Regularity

Abstract

The object of this paper is twofold. Firstly, we study a class of generalized Newtonian fluid related to "power law ". For the corresponding non-Newtonian Navier-Stokes problems, the existence of a weak and periodic solutions is proved in the large for a bounded domain in $\mathbb{R}^3$. Further, variational inequalities and local-in-time well-posedness of the initial-boundary value problem are investigated. Secondly, we deduce a generalization of the Graffi-Kazhikhov-Smagulov model based on an advective-diffusion process in the context of multiphase theory. Local-in-time well-posedness of the initial-boundary value problem is investigated