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

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.