Blow-up of solutions for relaxed compressible Navier-Stokes equations

TL;DR

This paper proves that solutions to certain relaxed compressible Navier-Stokes equations with large initial data can blow up in finite time, contrasting with classical models where solutions exist globally.

Contribution

It improves previous blow-up results by considering relaxed models that avoid boundary hyperbolicity, providing new examples of finite-time blow-up.

Findings

Large data solutions blow up in finite time in relaxed models

Contrasts with classical Navier-Stokes where solutions are global

Provides new insights into effects of relaxation on solution behavior

Abstract

We present a blow-up result for large data for relaxed compressible Navier-Stokes models avoiding the possibility of reaching the boundary of hyperbolicity. Thus a previous result is improved and further examples are given illustrating possible effects of a relaxation and contrasting the classical compressible Navier-Stokes equations without relaxation where solutions for large data exist globally.