Global solutions and uniform convergence stability for compressible Navier-Stokes equations with oldroyd-type constitutive law

TL;DR

This paper proves the global existence and convergence of solutions for a one-dimensional compressible Navier-Stokes system with Oldroyd-type constitutive law, highlighting stability and uniform convergence as relaxation time varies.

Contribution

It establishes uniform a priori estimates and demonstrates global solutions and convergence for the system with small initial data, extending classical results to Oldroyd-type models.

Findings

Global existence of smooth solutions for small initial data

Uniform convergence of the system to classical Navier-Stokes equations

Stability results with respect to relaxation time

Abstract

We consider one dimensional isentropic compressible Navier-Stokes equations with Oldroyd-type constitutive law. By establishing uniform a priori estimates (with respect to relaxation time), we show global existence of smooth solutions with small initial data. Moreover, we get global-in-time convergence of the system towards the classical isentropic compressible Navier-Stokes equations.