Mach limits in analytic spaces

TL;DR

This paper proves that solutions to the compressible Euler equations in analytic and Gevrey spaces converge to incompressible solutions as Mach number tends to zero, with uniform bounds in the respective norms.

Contribution

It establishes the Mach limit in analytic and Gevrey spaces for the Euler equations, providing uniform bounds and convergence results.

Findings

Solutions are uniformly bounded in analytic norms

Convergence to incompressible Euler solutions is proven in analytic norms

Results extend to Gevrey spaces with similar convergence

Abstract

We address the Mach limit problem for the Euler equations in the analytic spaces. We prove that, given analytic data, the solutions to the compressible Euler equations are uniformly bounded in a suitable analytic norm and then show that the convergence toward the incompressible Euler solution holds in the analytic norm. We also show that the same results hold more generally for Gevrey data with the convergence in the Gevrey norms.