Multiple scales and singular limits of perfect fluids

In this article our goal is to study the singular limits for a scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach number $=\epsilon^m$, Rossby number $=\epsilon$ and Froude number $=\epsilon^n$ are proportional to a small parameter $\epsilon\rightarrow 0$. The fluid is confined to an infinite slab, the limit behaviour is identified as the incompressible Euler system. For \emph{well--prepared} initial data, the convergence is shown on the life span time interval of the strong solutions of the target system, whereas a class of generalized \emph{dissipative solutions} is considered for the primitive system. The technique can be adapted to the compressible Navier--Stokes system in the subcritical range of the adiabatic exponent $\gamma$ with $1<\gamma\leq\frac{3}{2}$, where the weak solutions are not known to exist.