Global existence of weak solutions to macroscopic models of polymeric flows
type: Item
instance of: scholarly article
title: Global existence of weak solutions to macroscopic models of polymeric flows
zbMATH Open document ID: 1239.35112
author: Nader Masmoudi
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2011-12-07T00:00:00Z
review text: The finite extensible nonlinear elastic (FENE) model, introduced by Peterlin describing a complex mixture of polymer and liquid is considered. The main result of this paper concerns the proof of the global existence of weak solutions of this model. An important problem is pointed out: the obtained results can be extended to the Oldroyd-B model, corresponding to the Hoken spring model at the microscopic level, when the extra stress tensor \(\tau\) belongs to \(L^2\). Even if in general this condition is not verified, the author proves in the last part a global existence theorem for a modified Oldroyd-B model that yields an \(L^2\) bound of \(\tau\). The main mathematical tool is the approximation of the initial system by a sequence of more regular problems (for which the existence is easily proved) and the use of a weak compactness argument. This point is rigorously analysed in section 3, also related to the Chacon limit (briefly recalled in the Appendix).
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 82D60
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 5986957
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: FENE-P model
zbMATH Keywords: micro-macro interactions
zbMATH Keywords: global existence
zbMATH Keywords: defect measure
reviewed by: Gelu Paşa
MaRDI profile type: Publication
full work available at URL: j.matpur.2011.04.008
OpenAlex ID: W2061265555
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DOI: 10.1016/J.MATPUR.2011.04.008
description: scientific article; zbMATH DE number 5986957