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arXiv · 2504.17290

Incompressible and fast rotation limits for 3D compressible rotating Euler system with general initial data

Mikihiro Fujii·Yang Li·Pengcheng Mu
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Abstract

This paper is concerned with the low Mach and Rossby number limits of $3$D compressible rotating Euler equations with ill-prepared initial data in the whole space. More precisely, the initial data is the sum of a $3$D part and a $2$D part. With the help of a suitable intermediate system, we perform this singular limit rigorously with the target system being a $2$D QG-type. This particularly gives an affirmative answer to the question raised by Ngo and Scrobogna [\emph{Discrete Contin. Dyn. Syst.}, 38 (2018), pp. 749-789]. As a by-product, our proof gives a rigorous justification from the $2$D inviscid rotating shallow water equations to the $2$D QG equations in whole space.

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Mikihiro Fujii, Yang Li, Pengcheng Mu. 2025-04-24. Incompressible and fast rotation limits for 3D compressible rotating Euler system with general initial data. https://arxiv.org/abs/2504.17290

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