# Global well-posedness for the Phan-Thein-Tanner model in critical Besov spaces without damping

## TL;DR

This paper establishes the global well-posedness of the Phan-Thein-Tanner model in critical Besov spaces for small initial data, extending understanding of polymeric fluid dynamics without damping effects.

## Contribution

It proves the global existence and uniqueness of solutions in critical Besov spaces for the PTT model without damping, a novel result in the mathematical analysis of polymeric fluids.

## Key findings

- Global well-posedness for small initial data
- Solutions exist in critical Besov spaces
- No damping required for stability

## Abstract

In this paper, we mainly investigate the Cauchy problem for the Phan-Thein-Tanner (PTT) model. The PPT model can be viewed as a Navier-Stokes equations couple with a nonlinear transport system. This model is derived from network theory for the polymeric fluid. We study about the global well posedness of the PTT model in critical Besov spaces. When the initial data is a small perturbation over around the equilibrium, we prove that the strong solution in critical Besov spaces exists globally.