Global Classical Solutions to a Compressible Model for Micro-Macro Polymeric Fluids Near Equilibrium

Global existence of weak solutions to some micro - macro models

We prove global existence of weak solutions for the co-rotational FENE dumbbell model and the Doi model also called the Rod model. The proof is based on propagation of compactness, namely if we take a sequence of weak solutions which converges weakly and such that the initial data converges strongly then the weak limit is also a solution. To cite this article: A. Name1, A. Name2, C. R. Acad. Sc...

On a variance reduction technique for the micro-macro simulations of polymeric fluids

The micro-macro simulations of polymeric fluids couple the mass and momentum conservation equations at the macroscopic level, with a stochastic differential equation which models the evolution of the polymer configurations at the microscopic level (Brownian dynamics simulation). Accordingly, the system is discretized by a finite element method coupled with a Monte Carlo method. All the discrete...

Dampening General Equilibrium: from Micro to Macro*

We argue that standard modeling practices often overstate the potency of general-equilibrium (GE) mechanisms. We formalize the notion that GE adjustment is weak, or that it takes time, by modifying an elementary Walrasian economy in two alternative manners. In one, we replace Rational Expectations Equilibrium with solution concepts that mimic Tâtonnement or Cobweb dynamics, Level-k Thinking, Re...

On Some Pdf Based Moment Closure Approximations of Micro-macro Models for Viscoelastic Polymeric Fluids

In this paper we will discuss several issues related to the moment-closure approximation of multiscale models for viscoelastic polymeric fluids. These moment-closure approaches are based on special ansatz for the probability density function (PDF) in the finite extensible nonlinear elastic (FENE) dumbbell micro-macro models which consists of the coupled incompressible Navier-Stokes equations an...

Mathematical Analysis of a Stochastic Differential Equation Arising in the Micro-macro Modelling of Polymeric Fluids