Global large solutions and incompressible limit for the compressible Navier-Stokes equations

TL;DR

This paper extends the analysis of the compressible Navier-Stokes equations to a critical $L^p$ framework, establishing the existence of global large solutions from highly oscillating initial velocities and exploring the incompressible limit.

Contribution

It generalizes previous $L^2$ results to a critical $L^p$ setting, providing new insights into large solutions and the incompressible limit for the equations.

Findings

Existence of global large solutions from highly oscillating initial velocities.

Extension of previous $L^2$ results to a critical $L^p$ framework.

Analysis of the incompressible limit in this new setting.

Abstract

The present paper is dedicated to the global large solutions and incompressible limit for the compressible Navier-Stokes system in $\mathbb{R}^d$ with $d\ge 2$. We aim at extending the work by Danchin and Mucha (Adv. Math., 320, 904--925, 2017) in $L^2$ structure to that in a critical $L^p$ framework. The result implies the existence of global large solutions initially from large highly oscillating velocity fields.