### 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 language | English (US) |
---|---|

Pages (from-to) | 427-500 |

Number of pages | 74 |

Journal | Inventiones Mathematicae |

Volume | 191 |

Issue number | 2 |

DOIs | |

State | Published - 2013 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

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

Research output: Contribution to journal › Article

*Inventiones Mathematicae*, vol. 191, no. 2, pp. 427-500. https://doi.org/10.1007/s00222-012-0399-y

}

TY - JOUR

T1 - Global existence of weak solutions to the FENE dumbbell model of polymeric flows

AU - Masmoudi, Nader

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84872772898&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872772898&partnerID=8YFLogxK

U2 - 10.1007/s00222-012-0399-y

DO - 10.1007/s00222-012-0399-y

M3 - Article

AN - SCOPUS:84872772898

VL - 191

SP - 427

EP - 500

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

IS - 2

ER -