Convergence rate of solutions toward stationary solutions to the isentropic micropolar fluid model in a half line

TL;DR

This paper analyzes how solutions to the one-dimensional compressible isentropic micropolar fluid model in a half line approach stationary solutions over time, establishing convergence rates and stability using weighted energy methods.

Contribution

It provides the first detailed analysis of convergence rates and stability for this specific micropolar fluid model in a half line setting.

Findings

Global solutions converge to stationary solutions at explicit rates.

Convergence is established for initial data in weighted Sobolev spaces.

Microrotational velocity influences the viscous behavior and stability.

Abstract

In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the one-dimensional compressible isentropic micropolar fluid model in a half line \mathbb{R}_{+}:=(0,\infty). We mainly investigates the unique existence, the asymptotic stability and convergence rates of stationary solutions to the outflow problem for this model. We obtain the convergence rates of global solutions towards corresponding stationary solutions if the initial perturbation belongs to the weighted Sobolev space. The proof is based on the weighted energy method by taking into account the effect of the microrotational velocity on the viscous compressible fluid.