Low Mach and thin domain limit for the compressible Euler system

We consider the compressible Euler system describing the motion of an ideal fluid confined to a straight layer ${\mathrm{\Omega }}_{\delta }=(0,\delta )\times {\mathbb{R}}^2,\delta >0$. In the framework of dissipative measure-valued solutions, we show the convergence to the strong solution of the 2D incompressible Euler system when the Mach number tends to zero and $\delta \to 0$.