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

Abstract

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.

Global strong solutions and optimal $L^2$ decay to the compressible FENE dumbbell model

“…In the co-rotation case with d = 2, he [28] obtained a global result for k > 0 without any small conditions. In the co-rotation case, A. V. Busuioc, I. S. Ciuperca, D. Iftimie and L. I. Palade [5] obtained a global existence result with only the small condition on ψ 0 . The global existence of weak solutions in L 2 was proved recently by N. Masmoudi [29] under some entropy conditions.…”

Large time behavior of global strong solutions to the 2-D compressible FENE dumbbell model

“…In the co-rotation case with d = 2, he [31] obtained a global result for k > 0 without any small conditions. A. V. Busuioc, I. S. Ciuperca, D. Iftimie and L. I. Palade [5] obtain a global existence result with only the small condition on ψ 0 . The global existence of weak solutions in L 2 was proved recently by N. Masmoudi [32] under some entropy conditions.…”

Global strong solutions and large time behavior to the compressible co-rotation FENE dumbbell model of polymeric flows near equilibrium

“…In the co-rotation case with d = 2, he [25] obtained a global result for k > 0 without any small conditions. In the co-rotation case, A. V. Busuioc, I. S. Ciuperca, D. Iftimie and L. I. Palade [4] obtained a global existence result with only the small condition on ψ 0 . The global existence of weak solutions in L 2 was proved recently by N. Masmoudi [26] under some entropy conditions.…”