Local Existence for the FENE-Dumbbell Model of Polymeric Fluids

We study the well-posedness of a multi-scale model of polymeric fluids. The microscopic model is the kinetic theory of the finitely extensible nonlinear elastic (FENE) dumbbell model. The macroscopic model is the incompressible non-Newton fluids with polymer stress computed via the Kramers expression. The boundary condition of the FENE-type Fokker-Planck equation is proved to be unnecessary by the singularity on the boundary. Other main results are the local existence, uniqueness and regularity theorems for the FENE model in certain parameter range.

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