Local energy decay of solutions to the linearized compressible viscoelastic system around motionless state in an exterior domain

TL;DR

This paper investigates how solutions to the linearized compressible viscoelastic equations decay over time in an exterior domain, revealing diffusion wave phenomena due to sound and shear waves.

Contribution

It provides the first local energy decay estimates for the linearized system in an exterior domain, highlighting the diffusion wave behavior caused by viscous and elastic effects.

Findings

Established local energy decay rates for the linearized system.

Identified diffusion wave phenomena in the decay process.

Connected decay behavior to sound and shear wave diffusion.

Abstract

We study the large time behavior of solutions to the system of equations describing motion of compressible viscoelastic fluids. We focus on the linearized system around a motionless state in a three-dimensional exterior domain and derive the local energy decay estimate of its solution to give the diffusion wave phenomena caused by sound wave viscous diffusion and elastic shear wave.