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

Rodolfo Salvi

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

Analysis of PDEs 2017-01-20 v2

Authors: Rodolfo Salvi

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

Keywords

non-Newtonian fluid Navier-Stokes equation phase field approach well-posedness variational inequality Graffi-Kazhikhov-Smagulov model

Cite

@article{arxiv.1610.00103,
  title  = {On Non-Newtonian fluids and phase field approach: Existence and Regularity},
  author = {Rodolfo Salvi},
  journal= {arXiv preprint arXiv:1610.00103},
  year   = {2017}
}

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