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

TL;DR

This paper proves the existence, uniqueness, and decay rates of strong solutions to a coupled compressible fluid and polymer model, advancing understanding of polymeric flow behavior near equilibrium in multiple dimensions.

Contribution

It establishes global well-posedness and optimal decay rates for the compressible co-rotation FENE dumbbell model near equilibrium, combining spectral theory and Hardy inequalities.

Findings

Existence of unique global strong solutions near equilibrium for dimensions d≥2.

Optimal decay rates for solutions in dimensions d≥3.

Application of spectral theory and Hardy inequalities to decay analysis.

Abstract

In this paper, we mainly study global well-posedness and optimal decay rate for the strong solutions of the compressible co-rotation finite extensible nonlinear elastic (FENE) dumbbell model. This model is a coupling of the isentropic compressible Navier-Stokes equations with a nonlinear Fokker-Planck equation. We first prove that the FENE dumbbell model admits a unique global strong solution provided the initial data are close to equilibrium state for $d\geq 2$. Moreover, for $d\geq3$, we show that optimal decay rates of global strong solutions by the linear spectral theory and a more precise Hardy type inequality.