Global solutions for micro-macro models of polymeric fluids

TL;DR

This paper presents a simpler and more direct proof for the global well-posedness of fluid-polymer systems in two dimensions, using the co-rotational FENE model and coupled equations as examples.

Contribution

It introduces a novel, more straightforward proof technique for the well-posedness of fluid-polymer models, improving upon existing methods.

Findings

Proves global well-posedness in 2D for coupled fluid-polymer systems

Simplifies the proof process compared to traditional methods

Validates approach with FENE and Smoluchowski-Navier-Stokes models

Abstract

We provide a new proof for the global well-posedness of systems coupling fluids and polymers in two space dimensions. Compared to the well-known existing method based on the losing a priori estimates, our method is more direct and much simpler. The co-rotational FENE dumbbell model and the coupling Smoluchowski and Navier-Stokes equations are studied as examples to illustrate our main ideas.