Open AccessMach limits in analytic spaces on exterior domains
Author(s) -
Juhi Jang,
Igor Kukavica,
Linfeng Li
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2022027
Subject(s) - mathematics , mach number , mathematical analysis , analytic function , limit (mathematics) , norm (philosophy) , euler's formula , domain (mathematical analysis) , boundary value problem , physics , political science , mechanics , law
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.