On self-similar solutions to degenerate compressible Navier-Stokes equations

TL;DR

This paper investigates special self-similar solutions to the compressible Navier-Stokes equations with density-dependent viscosity, establishing conditions for their existence and non-existence.

Contribution

It provides new mathematical results on the existence of expanders and the non-existence of small shrinkers for cavitating solutions in degenerate compressible flows.

Findings

Proved existence of expanders in certain regimes.

Proved non-existence of small shrinkers.

Characterized cavitating self-similar solutions.

Abstract

We study cavitating self-similar solutions to compressible Navier-Stokes equations with degenerate density-dependent viscosity. We prove both existence of expanders and non-existence of small shrinkers.