Integrability and regularity of 3D Euler and equations for uniformly rotating fluids
type: Item
instance of: scholarly article
title: Integrability and regularity of 3D Euler and equations for uniformly rotating fluids
zbMATH Open document ID: 0867.76012
DOI: 10.1016/0898-1221(96)00040-5
author: A. Babin
author: Alex Mahalov
author: Basil Nicolaenko
publication date: 1997-08-14T00:00:00Z
review text: The authors consider the periodic solutions of the classical Euler equations for incompressible fluids with the additional term \(2\Omega JU\) in the equation of dynamics. This Coriolis force term is responsible for uniform rotation of fluids. It is shown that solutions can be decomposed into three summands, the first one is a solution of the two-dimensional Euler system with vertically averaged initial data, the second one is related to a solution of a new system, and the third summand is a remainder of the \(\text{Ro}^{1/2}\) order where Ro is with the anisotropic Rossby number Ro. A number of theorems for sufficiently smooth initial data are claimed without proof, including existence of regular solutions on the time interval depending on the Rossby number. This interval goes to infinity as \(\text{Ro}\to 0\).
Mathematics Subject Classification ID: 76B47
Mathematics Subject Classification ID: 76U05
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 915122
zbMATH Keywords: periodic solutions
zbMATH Keywords: Coriolis force term
zbMATH Keywords: vertically averaged initial data
zbMATH Keywords: anisotropic Rossby number
zbMATH Keywords: smooth initial data
zbMATH Keywords: existence of regular solutions
reviewed by: P. B. Dubovski
MaRDI profile type: Publication
full work available at URL: 0898-1221(96)00040-5
OpenAlex ID: W1964507245
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 915122