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Funktsional'nyi Analiz i ego Prilozheniya, 2003, Volume 37, Issue 3, Pages 77–80
DOI: https://doi.org/10.4213/faa160 (Mi faa160) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Brief communications

An Analytic Proof of the Nonintegrability of the ABC-flow for $A=B=C$

S. L. Ziglin

Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences
Full-text PDF (130 kB) Citations (11)
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DOI: https://doi.org/10.4213/faa160
Abstract: We prove the absence of a real-analytic first integral in a known system describing the stationary flow of an ideal incompressible fluid with periodic boundary conditions and with velocity field collinear to the rotor of itself (an ABC-flow) for the case in which all three parameters occurring in the system are equal. A computer proof of this fact was previously known.
Keywords: ABC-flow, monodromy group, fundamental group.
Received: 01.10.2001
English version:
Functional Analysis and Its Applications, 2003, Volume 37, Issue 3, Pages 225–227
DOI: https://doi.org/10.1023/A:1026040802018
Bibliographic databases:
Document Type: Article
UDC: 517.913
Language: Russian
Citation: S. L. Ziglin, “An Analytic Proof of the Nonintegrability of the ABC-flow for $A=B=C$”, Funktsional. Anal. i Prilozhen., 37:3 (2003), 77–80; Funct. Anal. Appl., 37:3 (2003), 225–227
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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