A remark on the stability problem in fluid dynamics
type: Item
instance of: scholarly article
title: A remark on the stability problem in fluid dynamics
zbMATH Open document ID: 0626.76056
DOI: 10.1016/0022-247X(87)90193-4
author: Vinicio Moauro
author: Carlo Marchioro
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: We show how one of the mentioned \textit{V. I. Arnold}'s results [e.g.: Mathematical methods of classical mechanics (1978; Zbl 0386.70001)] can be extended to some limit cases which are nontrivial from a physical point of view. The result will be obtained by constructing a one- parameter family of auxiliary functions which assures the stability of the stationary flow. Arnold's procedure has been used in more general problems of the physics of fluids and plasmas. We think that, also in these problems, the approach proposed here could be useful. Finally, we remark that other methods have been used to study the stability problem for fluids and plasmas getting results which have some overlap with the present one.
Mathematics Subject Classification ID: 76E25
Mathematics Subject Classification ID: 76X05
Mathematics Subject Classification ID: 76A02
zbMATH DE Number: 4018637
zbMATH Keywords: direct method
zbMATH Keywords: Liapunov theorem
zbMATH Keywords: one-parameter family of auxiliary functions
zbMATH Keywords: stability
MaRDI profile type: Publication
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full work available at URL: 0022-247x(87)90193-4
OpenAlex ID: W2028616250
description: scientific article; zbMATH DE number 4018637