Mathematical existence results for the Doi-Edwards polymer model

TL;DR

This paper provides rigorous mathematical proofs of the existence, uniqueness, and global-in-time solutions for the Doi-Edwards polymer model, a complex coupled system describing polymer dynamics.

Contribution

It offers the first rigorous proof of well-posedness and global solutions for the Doi-Edwards model in two dimensions, advancing mathematical understanding of polymer flow models.

Findings

Proved existence and uniqueness of solutions.

Established global-in-time solutions in 2D without small data restrictions.

Enhanced mathematical foundation for the Doi-Edwards model.

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 tested extensively 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 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.