The FENE Dumbbell Polymer Model: Existence and Uniqueness of Solutions for the Momentum Balance Equation

We consider the FENE dumbbell polymer model which is the coupling of the incompressible Navier-Stokes equations with the corresponding Fokker–Planck–Smoluchowski diffusion equation. We show global well-posedness in the case of a 2D bounded domain. We assume in the general case that the initial veloc...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2014-06, Vol.26 (2), p.217-241
Main Authors: Busuioc, Adriana Valentina, Ciuperca, Ionel Sorin, Iftimie, Dragoş, Palade, Liviu Iulian
Format: Article
Language:English
Subjects:
Analysis of PDEs
Applications of Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary:We consider the FENE dumbbell polymer model which is the coupling of the incompressible Navier-Stokes equations with the corresponding Fokker–Planck–Smoluchowski diffusion equation. We show global well-posedness in the case of a 2D bounded domain. We assume in the general case that the initial velocity is sufficiently small and the initial probability density is sufficiently close to the equilibrium solution; moreover an additional condition on the coefficients is imposed. In the corotational case, we only assume that the initial probability density is sufficiently close to the equilibrium solution.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-014-9369-y