Multiscale Analysis in the Compressible Rotating and Heat Conducting Fluids

We consider the full Navier–Stokes–Fourier system under rotation in the singular regime of small Mach and Rossby, and large Reynolds and Péclet numbers, with ill prepared initial data on an infinite straight 3-D layer rotating with respect to the axis orthogonal to the layer. We perform the singular limit in the framework of weak solutions and identify the 2-D Euler–Boussinesq system as the target problem.