## Abstract

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_{B}T≥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.

Original language | English (US) |
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Pages (from-to) | 1304-1315 |

Number of pages | 12 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 68 |

Issue number | 5 |

DOIs | |

State | Published - Nov 6 2008 |

## All Science Journal Classification (ASJC) codes

- Applied Mathematics