Zero Mach Number Limit of the Compressible Primitive Equations: Ill-prepared Initial Data

2022/08/03 by Xin Liu, Liu, Xin, Edriss S. Titi +1 · 1 citation
Engineering · Mathematics · #35B25 #35B40 #76N10 #Analysis of PDEs (math.AP) #Atmospheric and Oceanic Physics (physics.ao-ph) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Navier-Stokes equation solutions #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2208.02329

openalex publication_date 2022/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the work, we consider the zero Mach number limit of compressible primitive equations in the domain ℝ² × 2\mathbbT or \mathbbT² × 2\mathbbT. We identify the limit equations to be the primitive equations with the incompressible condition. The convergence behaviors are studied in both ℝ² × 2\mathbbT and \mathbbT² × 2\mathbbT, respectively. This paper takes into account the high oscillating acoustic waves and is an extension of our previous work by X. Liu and E.S. Titi, Arch. Rational Mech. Anal., 238, 705-747, 2020.

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