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 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.

References in corpus (2)

• Existence and equilibration of global weak solutions to finitely extensible nonlinear bead-spring chain models for dilute polymers
• Global existence of weak solutions to the FENE dumbbell model of polymeric flows

Cited by in corpus (9)

• The $L^2$ decay for the 2D co-rotation FENE dumbbell model of polymeric flows
• Analysis of a dilute polymer model with a time-fractional derivative
• New Temperature Dependent Configurational Probability Diffusion Equation For Diluted FENE Polymer Fluids: Existence of Solution Results
• Global strong solutions and optimal $L^2$ decay to the compressible FENE dumbbell model
• On the Doi-Edwards and K-BKZ rheological models for polymer fluids: an existence result for shear flows
• Vanishing viscosity limit to the FENE dumbbell model of polymeric flows
• Large time behavior of global strong solutions to the 2-D compressible FENE dumbbell model
• Global strong solutions and large time behavior to the compressible co-rotation FENE dumbbell model of polymeric flows near equilibrium
• Large time behavior to the FENE dumbbell model of polymeric flows near equilibrium