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Equations for Polymeric Materials

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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

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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.

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Authors and Affiliations

  1. Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer street, NY 10012, NY, USA

    Nader Masmoudi

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  1. Nader Masmoudi
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Correspondence to Nader Masmoudi .

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  1. Tokyo, Tokyo, Japan

    Yoshikazu Giga

  2. Toulon, Var, France

    Antonin Novotny

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Masmoudi, N. (2016). Equations for Polymeric Materials. In: Giga, Y., Novotny, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-10151-4_23-1

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  • DOI: https://doi.org/10.1007/978-3-319-10151-4_23-1

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