Corotational Hookean models of dilute polymeric fluids: existence of global weak solutions, weak-strong uniqueness, equilibration and macroscopic closure

Journal article

We prove the existence of global weak solutions to the corotational Hookean dumbbell 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 parabolic 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 incompressible 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.

Authors: Dębiec, T; Süli, E

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Society for Industrial and Applied Mathematics
• Journal: SIAM Journal on Mathematical Analysis
• Volume: 55
• Issue: 1
• Pages: 310-346
• Publication date: 2023-02-02
• Acceptance date: 2022-08-26
• DOI: 10.1137/22M149867X
• EISSN: 1095-7154
• ISSN: 0036-1410
• Language: English
• Keywords: kinetic polymer models; Navier–Stokes–Fokker–Planck system; FFR; Oldroyd-B model; relative energy method; existence of weak solutions; Hookean dumbbell model