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