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We investigate the well-posedness of a coupled Navier-Stokes-Fokker-Plancksystem with a time-fractional derivative. Such systems arise in the kinetictheory of dilute solutions of polymeric liquids, where the motion ofnoninteracting polymer chains in a Newtonian solvent is modelled by astochastic process exhibiting power-law waiting time, in order to capturesubdiffusive processes associated with non-Fickian diffusion. We outline thederivation of the model from a subordinated Langevin equation. The elasticproperties of the polymer molecules immersed in the solvent are modelled by afinitely extensible nonlinear elastic (FENE) dumbbell model, and the drag termin the Fokker--Planck equation is assumed to be corotational. We prove theglobal-in-time existence of large-data weak solutions to this time-fractionalmodel of order $\alpha \in (\tfrac12,1)$, and derive an energy inequalitysatisfied by weak solutions.

Analysis of a dilute polymer model with a time-fractional derivative