Global existence of weak solutions to macroscopic models of polymeric flows

Nader Masmoudi

doi:10.1016/j.matpur.2011.04.008

Global existence of weak solutions to macroscopic models of polymeric flows

Research output: Contribution to journal › Article › peer-review

Abstract

One of the most classical closures approximation of the FENE model of polymeric flows is the one proposed by Peterlin, namely the FENE-P model. We prove global existence of weak solutions to the FENE-P model. The proof is based on the propagation of some defect measures that control the lack of strong convergence in an approximating sequence. Using a similar argument, we also prove global existence of weak solutions to the Giesekus and the Phan-Thien and Tanner models.

Original language	English (US)
Pages (from-to)	502-520
Number of pages	19
Journal	Journal des Mathematiques Pures et Appliquees
Volume	96
Issue number	5
DOIs	https://doi.org/10.1016/j.matpur.2011.04.008
State	Published - Nov 2011

Keywords

Defect measure
FENE-P model
Global existence
Micro-macro interactions
Navier-Stokes equations

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1016/j.matpur.2011.04.008

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title = "Global existence of weak solutions to macroscopic models of polymeric flows",

abstract = "One of the most classical closures approximation of the FENE model of polymeric flows is the one proposed by Peterlin, namely the FENE-P model. We prove global existence of weak solutions to the FENE-P model. The proof is based on the propagation of some defect measures that control the lack of strong convergence in an approximating sequence. Using a similar argument, we also prove global existence of weak solutions to the Giesekus and the Phan-Thien and Tanner models.",

keywords = "Defect measure, FENE-P model, Global existence, Micro-macro interactions, Navier-Stokes equations",

author = "Nader Masmoudi",

note = "Funding Information: The work of N.M. is partially supported by NSF-DMS grant 0703145. The author would like to thank P.-L. Lions for many discussions about these models.",

year = "2011",

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AU - Masmoudi, Nader

N1 - Funding Information: The work of N.M. is partially supported by NSF-DMS grant 0703145. The author would like to thank P.-L. Lions for many discussions about these models.

PY - 2011/11

Y1 - 2011/11

N2 - One of the most classical closures approximation of the FENE model of polymeric flows is the one proposed by Peterlin, namely the FENE-P model. We prove global existence of weak solutions to the FENE-P model. The proof is based on the propagation of some defect measures that control the lack of strong convergence in an approximating sequence. Using a similar argument, we also prove global existence of weak solutions to the Giesekus and the Phan-Thien and Tanner models.

AB - One of the most classical closures approximation of the FENE model of polymeric flows is the one proposed by Peterlin, namely the FENE-P model. We prove global existence of weak solutions to the FENE-P model. The proof is based on the propagation of some defect measures that control the lack of strong convergence in an approximating sequence. Using a similar argument, we also prove global existence of weak solutions to the Giesekus and the Phan-Thien and Tanner models.

KW - Defect measure

KW - FENE-P model

KW - Global existence

KW - Micro-macro interactions

KW - Navier-Stokes equations

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M3 - Article

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JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 5

ER -

Global existence of weak solutions to macroscopic models of polymeric flows

Abstract

Keywords

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