Global existence of solutions for flows of fluids with pressure and shear dependent viscosities
type: Item
instance of: scholarly article
title: Global existence of solutions for flows of fluids with pressure and shear dependent viscosities
zbMATH Open document ID: 1062.76011
DOI: 10.1016/S0893-9659(02)00070-8
author: K. R. Rajagopal
author: Josef Málek
author: Jindřich Nečas
published in: Applied Mathematics Letters
publication date: 2003-03-10T00:00:00Z
review text: The equations of a viscous incompressible fluid are considered under the assumption that the viscosity \(\mu\) in the Stokes stress-strain law \(T=\) \(-pI+\) \(\mu D\) depends on the pressure \(p\) and on the invariant \(| D| \equiv\) \(\sqrt{D_{ij}D_{ij}}\) of the rate of strain tensor \(D\) in such a way that \(\partial\mu/\partial p >0\) and \(\partial\mu/\partial | D| <0\). A typical example is given by the formula \(\mu =\) \((\text{const}+\) \(\gamma (p)+\) \(| D| ^2)^{(r-2)/2}\). Here, \(\gamma =\) \(e^{-\alpha p}\) for large values of \(p\), and \(1<r<2\). The existence of weak space periodic solutions is discussed. It is proved that a solution can be obtained globally in time via the limit of a sequence of approximate solutions if they obey some natural a priori estimates.
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76A05
zbMATH DE Number: 1878910
zbMATH Keywords: weak space periodic solutions
zbMATH Keywords: convergence
reviewed by: V. V. Shelukhin
MaRDI profile type: Publication
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full work available at URL: s0893-9659(02)00070-8
OpenAlex ID: W1995539378
description: scientific article; zbMATH DE number 1878910