Time decay rates of non-Newtonian flows in \(\mathbf {R}^{n}_{+}\)
type: Item
instance of: scholarly article
title: Time decay rates of non-Newtonian flows in \(\mathbf {R}^{n}_{+}\)
zbMATH Open document ID: 1102.76014
author: Bo-Qing Dong
author: Zhi-Min Chen
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-11-15T00:00:00Z
review text: The authors study time decay rates for weak solutions to an incompressible non-Newtonian fluid model in \({\mathbb R}^{n}_{+}\) for \(n \geq 3\). The model is described by the so-called Ladyzhenskaya equations. Using the spectral decomposition of Stokes operator and \(L^{p}\)-\(L^{q}\) estimates, it can be shown that the weak solutions decay in \(L^{2}\) norm like \(t^{- {n \over 2} ({1 \over r} - {1 \over 2})}\) when the initial velocity \(u_{0} \in L^{2} \cap L^{r}\) for \(1 \leq r < 2\). If \(u_{0}\) satisfies additionally the momentum condition \[ \int_{{\mathbb R}^{n}_{+}} | x_{n} u_{0} (x)| ^{n} \,dx < \infty, \qquad 1 < r \leq 2, \] then the higher decay rates \(t^{- {n \over 2} ({1 \over r} - {1 \over 2}) - {1 \over 2}}\) are obtained. Furthermore, the difference between the non-Newtonian flow and Navier-Stokes flow is estimated.
reviewed by: Jürgen Socolowsky
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 5072987
zbMATH Keywords: spectral decomposition
zbMATH Keywords: weak solution
zbMATH Keywords: Ladyzhenskaya equations
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.12.070
OpenAlex ID: W2059718813
cites work: Existence and regularity of solutions of non-Newtonian flow
cites work: Decay rate for the incompressible flows in half spaces
cites work: On the regularity of flows with Ladyzhenskaya Shear-dependent viscosity and slip or non-slip boundary conditions
cites work: Q4273078
cites work: Young Measure‐Valued Solutions for Non-Newtonian Incompressible Fluids1
cites work: Q3199048
cites work: \(L^ 2\) decay for the Navier-Stokes flow in halfspaces
cites work: Partial regularity of suitable weak solutions of the navier-stokes equations
cites work: Large time behavior to the system of incompressible non-Newtonian fluids in \(\mathbb{R}^2\)
cites work: Analysis of a Ladyzhenskaya model for incompressible viscous flow
cites work: On estimates in Hardy spaces for the Stokes flow in a half space
cites work: Algebraic \(L^2\) decay for the solution to a class system of non-Newtonian fluid in \(\mathbb R^n\)
cites work: Partial regularity of suitable weak solutions to the system of the incompressible non-Newtonian fluids
cites work: Geometric theory of semilinear parabolic equations
cites work: Q5576913
cites work: Q5890172
cites work: Q4865486
cites work: \(L^2\) decay for weak solution to equations of non-Newtonian incompressible fluids in the whole space.
cites work: Cauchy problem for the non-Newtonian viscous incompressible fluid
cites work: \(L^ 2\) decay for weak solutions of the Navier-Stokes equations
cites work: Q4192429
cites work: A solution formula for the Stokes equation in Rn+
cites work: Decay Results for Weak Solutions of the Navier-Stokes Equations on Rn
DOI: 10.1016/J.JMAA.2005.12.070
description: scientific article; zbMATH DE number 5072987