Free surface problem of stationary non-Newtonian fluids
type: Item
instance of: scholarly article
title: Free surface problem of stationary non-Newtonian fluids
zbMATH Open document ID: 0967.76004
DOI: 10.1016/S0362-546X(98)00276-4
author: Hyeong-Ohk Bae
author: Kwon Cho
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-08-21T00:00:00Z
review text: The authors study a stationary free-surface problem for certain class of non-Newtonian fluids, called sometimes power-law fluids. They consider the viscous part of the stress tensor in the form \((\mu_0 + \mu_1|e(u)|^{p-2})e_{ij}(u)\), where \(e(u)\) is the symmetric part of the gradient of velocity \(u\), and \(1<p<\infty\). It is proved that in dimensions \(2\leq m\leq 5\) there exists a unique solution to the stationary free-surface problem provided that either \(\mu_0\) or \(\mu_1\) is sufficiently large or the forcing term is sufficiently small. The proof is based on a fixed point argument, and the upper bound for the space dimension comes from the requirement of compact imbedding of \(W^{1,2}\) into \(L^3\).
reviewed by: Milan Pokorný
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 1472256
zbMATH Keywords: non-Newtonian fluids
zbMATH Keywords: stationary free-surface problem
zbMATH Keywords: power-law fluids
zbMATH Keywords: fixed point argument
zbMATH Keywords: upper bound for space dimension
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
full work available at URL: s0362-546x(98)00276-4
OpenAlex ID: W2072461217
description: scientific article; zbMATH DE number 1472256