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Local existence for the FENE-dumbbell model of polymeric fluids. (English) Zbl 1095.76004
Summary: 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 describes incompressible non-Newtonian fluids with polymer stress computed via Kramers expression. The boundary condition of the FENE-type Fokker-Planck equation is proved to be unnecessary due to the singularity on the boundary. Other results are the local existence, uniqueness and regularity theorems for the FENE model in certain parameter range.

MSC:
76A10 Viscoelastic fluids
35Q35 PDEs in connection with fluid mechanics
82D60 Statistical mechanical studies of polymers
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