The incompressible limit of the isentropic fluids in the analytic spaces

TL;DR

This paper investigates the low Mach number limit of Euler equations for isentropic fluids within analytic and Gevrey spaces, establishing uniform bounds and convergence to incompressible flow for general initial data.

Contribution

It extends previous work to more general pressure laws and demonstrates uniform bounds and convergence in analytic and Gevrey norms for the incompressible limit.

Findings

Uniform bounds on solutions independent of the Mach number

Convergence to incompressible flow in analytic norm

Extension to more general pressure laws

Abstract

We consider the low Mach number limit problem of the Euler equations for isentropic fluids in the analytic spaces. We prove that, given general analytic initial data, the solution is uniformly bounded on a time interval independent of the small parameter and the incompressible limit holding in the analytic norm. The same results extend more generally to Gevrey initial data with convergence holds in a Gevrey norm. The results extend the isentropic fluids in arXiv:2102.11454 to more general pressure laws.