Vortex-like finite-energy asymptotic profiles for isentropic compressible flows

TL;DR

This paper extends the understanding of vortex-like structures in finite-energy, near-equilibrium isentropic compressible flows, building on prior work to describe their asymptotic profiles.

Contribution

It introduces a novel extension of asymptotic behavior descriptions from incompressible flows to finite-energy compressible flows with vortex structures.

Findings

Characterization of vortex-like finite-energy asymptotic profiles

Extension of previous asymptotic descriptions to compressible flows

Identification of vortex structures in near-equilibrium flows

Abstract

Bidimensional incompressible viscous flows with well-localised vorticity are well-known to develop vortex structures. The purpose of the present paper is to recover the asymptotic profiles describing these phenomena for homogeneous finite-energy flows as asymptotic profiles for near-equilibrium isentropic compressible flows. This task is performed by extending the sharp description of the asymptotic behaviour of near-equilibrium compressible flows obtained by David Hoff and Kevin Zumbrun to the case of finite-energy vortex-like solutions.