On diffusive 2D Fokker-Planck-Navier-Stokes systems

TL;DR

This paper establishes the global existence, uniqueness, and decay properties of solutions for diffusive kinetic models of polymeric fluids coupled with fluid dynamics, including a rigorous derivation of the Oldroyd-B model.

Contribution

It introduces a new solution framework based on moments, proves key properties for a broad class of initial data, and rigorously derives the Oldroyd-B closure from kinetic models.

Findings

Global existence and uniqueness of solutions

Decay of free energy over time

Rigorous derivation of Oldroyd-B model

Abstract

We study models kinetic models of polymeric fluids. We introduce a notion of solutions which is based on moments of polymeric distributions. We prove global existence and uniqueness of a large class of initial data for diffusive systems of kinetic equations coupled to fluid equations. As a corollary, we obtain a rigorous derivation of Oldroyd-B closure. We also prove decay of free energy for all the systems considered.