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arXiv · 2208.02329

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

Xin Liu·Edriss S. Titi
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Abstract

In the work, we consider the zero Mach number limit of compressible primitive equations in the domain $\mathbb{R}^2 \times 2\mathbb{T}$ or $\mathbb{T}^2 \times 2\mathbb{T}$. We identify the limit equations to be the primitive equations with the incompressible condition. The convergence behaviors are studied in both $\mathbb{R}^2 \times 2\mathbb{T}$ and $\mathbb{T}^2 \times 2\mathbb{T}$, 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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Xin Liu, Edriss S. Titi. 2022-08-03. Zero Mach Number Limit of the Compressible Primitive Equations: Ill-prepared Initial Data. https://arxiv.org/abs/2208.02329

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