Equations for polymeric materials

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationHandbook of Mathematical Analysis in Mechanics of Viscous Fluids
PublisherSpringer International Publishing
Pages973-1005
Number of pages33
ISBN (Electronic)9783319133447
ISBN (Print)9783319133430
DOIs
Publication statusPublished - Apr 19 2018

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ASJC Scopus subject areas

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

Cite this

Masmoudi, N. (2018). Equations for polymeric materials. In 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