The FENE dumbbell polymer model: existence and uniqueness of solutions for the momentum balance equation

The FENE dumbbell polymer model: existence and uniqueness of solutions for the momentum balance equation. A.V. Busuioc, I.S. Ciuperca, D. Iftimie and L.I. Palade Abstract We consider the FENE dumbbell polymer model which is the coupling of the incompress- ible 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 den- sity 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. Keywords: Navier-Stokes equations; FENE dumbbell chains; Fokker-Planck-Smoluchowski diffusion equation; existence and uniqueness of solutions. AMS subject classification: Primary 76D05; Secondary 35B40 1 Introduction The success of Kirkwood, and of Bird, Curtiss, Armstrong and Hassager (and their collabora- tors) kinetic theory of macromolecular dynamics triggered a still on-going flurry of activity aimed to providing molecular explanations for non-Newtonian and viscoelastic flow patterns. This can be reckoned from [BAH87] and [Ott06], for example. The cornerstone is the so called diffusion equation, a parabolic-type Fokker-Planck-Smoluchowski partial differential equation, the solution of which is the configurational probability distribution function; the later is the key ingredient for calculating the stress tensor.

• corotational model


• fokker-planck-smoluchowski diffusion equation


• following smallness


• fene dumbbell


• related physical constants


• fene fluid


• arbitrarily large initial