MACH LIMITS IN ANALYTIC SPACES ON EXTERIOR DOMAINS

We address the Mach limit problem for the Euler equations in an exterior domain with an analytic boundary. We first prove the existence of tangential analytic vector fields for the exterior domain with constant analyticity radii and introduce an analytic norm in which we distinguish derivatives taken from different directions. Then we prove the uniform boundedness of the solutions in the analytic space on a time interval independent of the Mach number, and Mach limit holds in the analytic norm. The results extend more generally to Gevrey initial data with convergence in a Gevrey norm.

Automated summary

This paper addresses the Mach limit problem for the Euler equations in an exterior domain with an analytic boundary. The authors prove the existence of tangential analytic vector fields and introduce an analytic norm for the exterior domain. They also demonstrate the uniform boundedness of solutions in the analytic space and establish the Mach limit holds in the analytic norm. These results are further extended to Gevrey initial data with convergence in a Gevrey norm.