Mach limits in analytic spaces on exterior domains

Juhi Jang; Igor Kukavica; Linfeng Li

doi:10.3934/dcds.2022027

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2022, Volume 42, Issue 8: 3629-3659. Doi: 10.3934/dcds.2022027

This issue Previous Article Next Article On the long-time behavior for a damped Navier-Stokes-Bardina model

Mach limits in analytic spaces on exterior domains

Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA

^*Corresponding author
^*Corresponding author

Received: July 1, 2021

Revised: January 1, 2022

Early access: March 23, 2022

Published online: March 23, 2022

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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