Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows

TL;DR

This paper proves the global existence of strong solutions for 3D compressible viscoelastic flows near equilibrium and establishes their optimal decay rates in various norms.

Contribution

It demonstrates the global existence of solutions under near-equilibrium conditions and derives their optimal decay rates, including in $L^p$ and $L^2$ norms.

Findings

Global existence of strong solutions near equilibrium

Optimal decay rates in $L^p$ and $L^2$ norms

Solutions converge to equilibrium at optimal rates

Abstract

In this paper, we are concerned with the global existence and optimal rates of strong solutions for three-dimensional compressible viscoelastic flows. We prove the global existence of the strong solutions by the standard energy method under the condition that the initial data are close to the constant equilibrium state in $H^2$-framework. If additionally the initial data belong to $L^1$, the optimal convergence rates of the solutions in $L^p$-norm with $2\leq p\leq 6$ and optimal convergence rates of their spatial derivatives in $L^2$-norm are obtained.