On the dimension of the attractor for a class of fluids with pressure dependent viscosities
type: Item
instance of: scholarly article
title: On the dimension of the attractor for a class of fluids with pressure dependent viscosities
zbMATH Open document ID: 1125.37057
published in: Communications on Pure and Applied Analysis
publication date: 2006-01-23T00:00:00Z
review text: The authors consider two-dimensional flows of an incompressible non-Newtonian fluid where the difference from the Navier-Stokes fluid is due to the viscosity depending on both the rate of deformation and the pressure. They prove the global existence and uniqueness of weak solutions. The authors establish the so-called ``smoothing property'' of the equation in the space of trajectories. Based on the last ``smoothing property'' they prove the existence of an exponential attractor and estimate its fractal dimension in terms of the data of the equation.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 37N10
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 5000544
zbMATH Keywords: large-time behaviour
zbMATH Keywords: fractal dimension
zbMATH Keywords: exponential attractor
author: Miroslav Bulíček
author: Josef Málek
author: Dalibor Pražák
MaRDI profile type: Publication
full work available at URL: cpaa.2005.4.805
OpenAlex ID: W1981510925
DOI: 10.3934/CPAA.2005.4.805
description: scientific article; zbMATH DE number 5000544