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Mathematical Existence Results for the Doi–Edwards Polymer Model

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Abstract

In this paper, we present some mathematical results on the Doi–Edwards model describing the dynamics of flexible polymers in melts and concentrated solutions. This model, developed in the late 1970s, has been used and extensively tested in modeling and simulation of polymer flows. From a mathematical point of view, the Doi–Edwards model consists in a strong coupling between the Navier–Stokes equations and a highly nonlinear constitutive law. The aim of this article is to provide a rigorous proof of the well-posedness of the Doi–Edwards model, namely that it has a unique regular solution. We also prove, which is generally much more difficult for flows of viscoelastic type, that the solution is global in time in the two dimensional case, without any restriction on the smallness of the data.

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Authors and Affiliations

  1. Laboratoire de Mathématiques CNRS-UMR 6620, Université Blaise Pascal, Clermont-Ferrand II, Campus des Cézeaux, 63177, Aubière Cedex, France

    Laurent Chupin

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  1. Laurent Chupin
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Correspondence to Laurent Chupin.

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Communicated by P. Constantin

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Chupin, L. Mathematical Existence Results for the Doi–Edwards Polymer Model. Arch Rational Mech Anal 223, 1–55 (2017). https://doi.org/10.1007/s00205-016-1030-y

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