Local well-posedness of the compressible FENE dumbbell model of Warner type

We consider a dilute suspension of dumbbells joined by finitely extendible nonlinear elastic connector evolving under the classical Warner potential , . The solvent consideration is modelled compressible Navier–Stokes system defined on torus with d = 2, 3 coupled Fokker–Planck equation (Kolmogorov forward equation) for probability density function dumbbell configuration. prove existence unique local-in-time solution to where this smooth in spacetime variables and interpreted weakly elongation variable. Our result holds true independently whether or not centre-of-mass diffusion term incorporated equation.