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

2016/10/01 by Salvi, Rodolfo
#35Q30 #35Q35 #35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.00103

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 ℝ³. 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

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