### Abstract

Systems coupling fluids and polymers are of great interest in many branches of sciences and engineering (applied physics, chemistry, biology, . . . ). These systems attempt to describe the behavior of complex mixtures of particles and fluids, and as such, they present numerous challenges, simultaneously at three levels: at the level of their derivation, the level of their numerical simulation, and that of their mathematical treatment. This chapter is devoted to the mathematical treatment after a brief discussion of the derivation of such models. Recent results about existence and uniqueness of strong solutions as well as global existence of weak solutions will be discussed. At the mathematical level, one of the main difficulties comes from the coupling of the Navier-Stokes system with a transport equation for the density of polymers.

Original language | English (US) |
---|---|

Title of host publication | Handbook of Mathematical Analysis in Mechanics of Viscous Fluids |

Publisher | Springer International Publishing |

Pages | 973-1005 |

Number of pages | 33 |

ISBN (Electronic) | 9783319133447 |

ISBN (Print) | 9783319133430 |

DOIs | |

State | Published - Apr 19 2018 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)
- Engineering(all)

### Cite this

*Handbook of Mathematical Analysis in Mechanics of Viscous Fluids*(pp. 973-1005). Springer International Publishing. https://doi.org/10.1007/978-3-319-13344-7_23

**Equations for polymeric materials.** / Masmoudi, Nader.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Handbook of Mathematical Analysis in Mechanics of Viscous Fluids.*Springer International Publishing, pp. 973-1005. https://doi.org/10.1007/978-3-319-13344-7_23

}

TY - CHAP

T1 - Equations for polymeric materials

AU - Masmoudi, Nader

PY - 2018/4/19

Y1 - 2018/4/19

N2 - Systems coupling fluids and polymers are of great interest in many branches of sciences and engineering (applied physics, chemistry, biology, . . . ). These systems attempt to describe the behavior of complex mixtures of particles and fluids, and as such, they present numerous challenges, simultaneously at three levels: at the level of their derivation, the level of their numerical simulation, and that of their mathematical treatment. This chapter is devoted to the mathematical treatment after a brief discussion of the derivation of such models. Recent results about existence and uniqueness of strong solutions as well as global existence of weak solutions will be discussed. At the mathematical level, one of the main difficulties comes from the coupling of the Navier-Stokes system with a transport equation for the density of polymers.

AB - Systems coupling fluids and polymers are of great interest in many branches of sciences and engineering (applied physics, chemistry, biology, . . . ). These systems attempt to describe the behavior of complex mixtures of particles and fluids, and as such, they present numerous challenges, simultaneously at three levels: at the level of their derivation, the level of their numerical simulation, and that of their mathematical treatment. This chapter is devoted to the mathematical treatment after a brief discussion of the derivation of such models. Recent results about existence and uniqueness of strong solutions as well as global existence of weak solutions will be discussed. At the mathematical level, one of the main difficulties comes from the coupling of the Navier-Stokes system with a transport equation for the density of polymers.

UR - http://www.scopus.com/inward/record.url?scp=85054346530&partnerID=8YFLogxK

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U2 - 10.1007/978-3-319-13344-7_23

DO - 10.1007/978-3-319-13344-7_23

M3 - Chapter

AN - SCOPUS:85054346530

SN - 9783319133430

SP - 973

EP - 1005

BT - Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

PB - Springer International Publishing

ER -