Existence of large-data global-in-time finite-energy weak solutions to a compressible FENE-P model

Abstract

A compressible FENE-P-type model with stress diffusion is derived from an approximate macroscopic closure of a compressible Navier–Stokes–Fokker–Planck system arising in the kinetic theory of dilute polymeric fluids, where polymer chains immersed in a barotropic, compressible, isothermal, viscous Newtonian solvent are idealised as pairs of massless beads connected with finitely extensible nonlinear elastic (FENE) springs. We develop a priori bounds for the model, including logarithmic bounds, which guarantee the non-negativity of the conformation tensor and a bound on its trace, and we prove the existence of large-data global-in-time finite-energy weak solutions in two and three space dimensions.