Singular limits of the compressible fluid models

Abstract: In this talk I explain the study of 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 \(\epsilon\rightarrow 0\) and \( m,n\in \mathbb{N} \). I consider the fluid is confined to an infinite slab, the limit behaviour is identified as the incompressible Euler system. For 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 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.