Global large solution to the compressible Navier-Stokes equations in critical Besov space ${\dot{B}}_{\mathrm{\infty },\mathrm{\infty }}^{-1}$

In this paper, we construct a class of global large solution to the compressible Navier-Stokes equations in the whole space ${\mathbb{R}}^d$. Precisely speaking, our choice of special initial data whose ${\dot{B}}_{\mathrm{\infty },\mathrm{\infty }}^{-1}$ norm can be arbitrarily large, namely, $\mathrm{\mid }\mathrm{\mid }{u}_0\mathrm{\mid }{\mathrm{\mid }}_{{\dot{B}}_{\mathrm{\infty },\mathrm{\infty }}^{-1}}\gg 1$, allows to give rise to global-in-time solution to the compressible Navier-Stokes equations.