Decay estimates for the compressible viscoelastic equations in an exterior domain

TL;DR

This paper establishes decay rates and $L_2$ estimates for solutions to the compressible viscoelastic equations in an exterior domain, advancing understanding of their long-term behavior.

Contribution

It provides the first decay estimates for nonlinear compressible viscoelastic equations in exterior domains, including optimal decay rates for solutions and derivatives.

Findings

Proved $L_2$ estimates for linearized problem solutions.

Established decay rates for nonlinear solutions.

Obtained optimal decay rates for solutions and derivatives.

Abstract

In this paper, we study the compressible viscoelastic equations in an exterior domain. We prove the $L_2$ estimates for the solution to the linearized problem and show the decay estimates for the solution to the nonlinear problem. In particular, we obtain the optimal decay rates of the solution itself and its spatial-time derivatives in the $L_2$-norm.