# Global classical solutions to a Compressible Model for Micro-Macro Polymeric Fluids Near Equilibrium

## TL;DR

This paper derives a coupled micro-macro model for compressible polymeric fluids using energetic variational methods and proves the global existence of smooth solutions near equilibrium.

## Contribution

It introduces a new coupled model for compressible polymeric fluids and establishes global existence results for solutions near equilibrium.

## Key findings

- Successful derivation of a coupled micro-macro model using energetic variational methods.
- Proof of global in time existence of smooth solutions near equilibrium.
- Demonstration of the model's well-posedness in the near-equilibrium regime.

## Abstract

In this paper we first employ the energetic variational method to derive a micro-macro model for compressible polymeric fluids. This model is a coupling of isentropic compressible Navier-Stokes equations with a nonlinear Fokker-Planck equation. We then prove the global in time existence of the smooth solution near the global equilibrium.