Existence of large-data global weak solutions to kinetic models of nonhomogeneous dilute polymeric fluids

We prove the existence of large-data global-in-time weak solutions to a general class coupled bead-spring chain models with finitely extensible nonlinear elastic (FENE) type spring potentials for nonhomogeneous incompressible dilute polymeric fluids in bounded domain $ \mathbb{R}^d $, d = 2 or 3 $. The under consideration involves Navier–Stokes system variable density, where viscosity coefficient depends on both density and polymer number Fokker–Planck equation density-dependent drag coefficient. proof is based combining truncation probability function two-stage Galerkin approximation compactness compensated techniques pass limits sequence approximations level.