COROTATIONAL HOOKEAN MODELS OF DILUTE POLYMERIC FLUIDS: EXISTENCE OF GLOBAL WEAK SOLUTIONS, WEAK-STRONG UNIQUENESS, EQUILIBRATION, AND MACROSCOPIC CLOSURE

We prove the existence of global weak solutions to the corotational Hookean dumb-bell model, a system of PDEs arising in the kinetic theory of dilute polymers, involving the unsteady incompressible Navier-Stokes equations in a bounded domain coupled to a Fokker-Planck type para-bolic equation including a center-of-mass diffusion term, satisfied by the probability density function, modeling the evolution of the configuration of noninteracting polymer molecules in a viscous incom-pressible solvent. The micro-macro interaction is manifested by the presence of a corotational drag term in the Fokker-Planck equation and the divergence of a polymeric extra-stress tensor on the right-hand side of the Navier-Stokes momentum equation. We also analyze certain properties of weak solutions to this system of PDEs: we use the relative energy method to deduce a weak-strong uniqueness type result, and derive the macroscopic closure of the kinetic model; a corotational Oldroyd-B model with stress-diffusion. Finally, we discuss the existence and uniqueness of global weak solutions to this class of corotational Oldroyd-B models with stress-diffusion.