Vanishing viscosity limit to the FENE dumbbell model of polymeric flows

TL;DR

This paper studies the inviscid limit of the FENE dumbbell model for polymeric flows, establishing uniform estimates, continuity of the solution map, and convergence to Euler-Fokker-Planck systems with rates.

Contribution

It provides the first rigorous analysis of the inviscid limit for the FENE dumbbell model using Besov space estimates and convergence rates.

Findings

Uniform estimates in Besov spaces for viscous solutions

Continuity of the data-to-solution map

Convergence to Euler-Fokker-Planck system with explicit rates

Abstract

In this paper we mainly investigate the inviscid limit for the strong solutions of the finite extensible nonlinear elastic (FENE) dumbbell model. By virtue of the Littlewood-Paley theory, we first obtain a uniform estimate for the solution to the FENE dumbbell model with viscosity in Besov spaces. Moreover, we show that the data-to-solution map is continuous. Finally, we prove that the strong solution of the FENE dumbbell model converges to a Euler system couple with a Fokker-Planck equation. Furthermore, convergence rates in Lebesgue spaces are obtained also.