ANALYSIS OF A DILUTE POLYMER MODEL WITH A TIME-FRACTIONAL DERIVATIVE.

We investigate the well-posedness of a coupled Navier-Stokes-Fbkker-Planck system with a time-fractional derivative. Such systems arise in the kinetic theory of dilute solutions of polymeric liquids, where the motion of noninteracting polymer chains in a Newtonian solvent is modeled by a stochastic process exhibiting power-law waiting time in order to capture Subdiflfusive processes associated with non-Fickian diffusion. We outline the derivation of the model from a subordinated Langevin equation. The elastic properties of the polymer molecules immersed in the solvent are modeled by a finitely extensible nonlinear elastic dumbbell model, and the drag term in the Fokker-Planck equation is assumed to be Corotational. We prove the global-in-time existence of large-data weak solutions to this time-fractional model of order a ∈ (∣, 1) and derive an energy inequality satisfied by weak solutions. [ABSTRACT FROM AUTHOR]