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

Adriana Valentina Busuioc (1) , Ionel Sorin Ciuperca (2) , Dragos Iftimie (1) , Liviu Iulian Palade (2)

1 EDPA - Équations aux dérivées partielles, analyse
2 MMCS - Modélisation mathématique, calcul scientifique

We consider the FENE dumbbell polymer model which is the coupling of the incompressible Navier-Stokes equations with the corresponding Fokker-Planck-Smoluchowski di ffusion 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 coeffcients is imposed. In the corotational case, we only assume that the initial probability density is sufficiently close to the equilibrium solution.

Keywords: existence and uniqueness of solutions

Keywords: Fokker-Planck-Smoluchowski diffusion equation; FENE dumbbell chains; existence and uniqueness of solutions.; Navier-Stokes equations

Domains: Analysis of PDEs [math.AP]

Adriana Valentina Busuioc, Ionel Sorin Ciuperca, Dragos Iftimie, Liviu Iulian Palade. The FENE dumbbell polymer model: existence and uniqueness of solutions for the momentum balance equation. Journal of Dynamics and Differential Equations, 2014, 26 (2), pp.217-241. ⟨10.1007/s10884-014-9369-y⟩. ⟨hal-00583748⟩