Compressible Navier--Stokes--Coriolis system in critical Besov spaces

We consider the three-dimensional compressible Navier--Stokes system with the Coriolis force and prove the long-time existence of a unique strong solution. More precisely, we show that for any $0<T<\infty$ and arbitrary large initial data in the scaling critical Besov spaces, the solution uniquely exists on $[0,T]$ provided that the speed of rotation is high and the Mach numbers are low enough. To the best of our knowledge, this paper is the first contribution to the well-posedness of the \textit{compressible} Navier--Stokes system with the Coriolis force in the whole space $\mathbb R^3$. The key ingredient of our analysis is to establish the dispersive linear estimates despite a quite complicated structure of the linearized equation due to the anisotropy of the Coriolis force.