Multiple scales and singular limits of perfect fluids

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