Boundary conditions for the microscopic fene models

We consider the microscopic equation of finite extensible nonlinear elasticity (FENE) models for polymeric fluids under a steady flow field. It is shown that for the underlying Fokker-Planck type of equations, anypreassigned distribution on the boundary will become redundant once the nondimensional number Li := Hb/κ_BT≥2, where H is the elasticity constant, √b is the maximum dumbbell extension, T is the temperature, and κ_B is the usual Boltzmann constant. Moreover, if the probability density functionis regularenough for its trace to be defined on the sphere |m| = √b, then the trace is necessarily zero when Li > 2. These results are consistent with our numerical simulations as well assome recent well-posedness results by preassuming a zero boundary distribution.