Global existence of weak solutions to the FENE dumbbell model of polymeric flows

Research output: Contribution to journalArticle

Abstract

Systems coupling fluids and polymers are of great interest in many branches of sciences. One of the most classical models to describe them is the FENE (Finite Extensible Nonlinear Elastic) dumbbell model. We prove global existence of weak solutions to the FENE dumbbell model of polymeric flows. The main difficulty is the passage to the limit in a nonlinear term that has no obvious compactness properties. The proof uses many weak convergence techniques. In particular it is based on the control of the propagation of strong convergence of some well chosen quantity by studying a transport equation for its defect measure. In addition, this quantity controls a rescaled defect measure of the gradient of the velocity.

Original languageEnglish (US)
Pages (from-to)427-500
Number of pages74
JournalInventiones Mathematicae
Volume191
Issue number2
DOIs
StatePublished - 2013

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Existence of Weak Solutions
Global Existence
Defects
Weak Convergence
Strong Convergence
Transport Equation
Compactness
Branch
Polymers
Model
Propagation
Gradient
Fluid
Term

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Global existence of weak solutions to the FENE dumbbell model of polymeric flows. / Masmoudi, Nader.

In: Inventiones Mathematicae, Vol. 191, No. 2, 2013, p. 427-500.

Research output: Contribution to journalArticle

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