# Singular limits for compressible inviscid rotating fluids

## TL;DR

This paper investigates the behavior of rotating, compressible inviscid fluids under singular limits, showing convergence to an incompressible system as the Mach and Rossby numbers tend to zero.

## Contribution

It introduces a general class of dissipative solutions for scaled compressible Euler systems and proves their convergence to an incompressible inviscid limit.

## Key findings

- Dissipative solutions converge to strong solutions of the incompressible system.
- The limit behavior is characterized as horizontal motion in an infinite slab.
- The analysis applies to a broad class of solutions, including weak solutions.

## Abstract

We study singular limit for scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach and Rossby numbers are proportional to a small parameter $\epsilon$. If the fluid is confined to an infinite slab, the limit behaviour is identified as a horizontal motion of an incompressible inviscid system that is analogous to the Euler system. We consider a very general class of solutions, named dissipative solution for the scaled compressible Euler systems and will show that it converges to a strong solution of that incompressible inviscid system.