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

TL;DR

This paper establishes the existence of unique global strong solutions and their optimal $L^2$ decay rates for the compressible FENE dumbbell model in multiple dimensions, advancing understanding of its long-term behavior.

Contribution

It proves global well-posedness near equilibrium and derives optimal decay rates using Littlewood-Paley and Fourier methods, which are novel in this context.

Findings

Existence of unique global strong solutions for $d extgreater 1$

Optimal $L^2$ decay rates for solutions when $d extgreater 2$

Application of Littlewood-Paley and Fourier splitting techniques

Abstract

In this paper, we are concerned with the global well-posedness and $L^2$ decay rate for the strong solutions of the compressible finite extensible nonlinear elastic (FENE) dumbbell model. For $d\geq 2$, we prove that the compressible FENE dumbbell model admits a unique global strong solution provided the initial data are close to equilibrium state. Moreover, by the Littlewood-Paley decomposition theory and the Fourier splitting method, we show optimal $L^2$ decay rate of global strong solutions for $d\geq 3$.