Global Well-posedness for the Three-Dimensional Generalized Phan–Thien–Tanner Model in Critical Besov Spaces

A new Generalized Phan–Thien–Tanner (GPTT) model is derived from a Lodge–Yamamoto type of network theory for the polymeric fluids. The GPTT model is developed to describe the rheological behavior of the viscoelastic fluids. In this paper, we investigate the initial-value problem for the GPTT model. Under the norm of the initial data is a small perturbation around some particular solution, we prove that the strong solution exists globally in critical Besov spaces.