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Mat. Zametki, 2016, Volume 99, Issue 4, Pages 626–630 (Mi mz11061)  

This article is cited in 9 scientific papers (total in 9 papers)

Brief Communications

Helicity is the Only Invariant of Incompressible Flows whose Derivative is Continuous in the $C^1$ Topology

E. A. Kudryavtseva

Lomonosov Moscow State University

Keywords: helicity, incompressible flow, exact divergence-free vector field, flux, topological invariants of magnetic fields.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-06302-а
Ministry of Education and Science of the Russian Federation НШ-7962.2016.1
This work was supported by the Russian Foundation for Basic Research under grant 15-01-06302-a and by the program “Leading Scientific Schools” under grant NSh-7962.2016.1.


DOI: https://doi.org/10.4213/mzm11061

Full text: PDF file (365 kB)
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English version:
Mathematical Notes, 2016, 99:4, 611–615

Bibliographic databases:

Received: 10.11.2015

Citation: E. A. Kudryavtseva, “Helicity is the Only Invariant of Incompressible Flows whose Derivative is Continuous in the $C^1$ Topology”, Mat. Zametki, 99:4 (2016), 626–630; Math. Notes, 99:4 (2016), 611–615

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. M. Akhmet'ev, E. A. Kudryavtseva, A. Yu. Smirnov, “A generalization of the arnol'd inequality in MHD”, Magnetohydrodynamics, 52:1-2 (2016), 5–14  isi
    2. A. Rechtman, P. Dehornoy, “The trunkenness of a volume-preserving vector field”, Nonlinearity, 30:11 (2017), 4089–4110  crossref  mathscinet  zmath  isi  scopus
    3. E. A. Kudryavtseva, “Continuous orbital invariants of integrable Hamiltonian systems”, Lobachevskii J. Math., 38:6 (2017), 1027–1041  crossref  mathscinet  zmath  isi  scopus
    4. D. Serre, “Helicity and other conservation laws in perfect fluid motion”, C. R. Mec., 346:3 (2018), 175–183  crossref  isi  scopus
    5. O. Bogoyavlenskij, “Invariants of the axisymmetric plasma flows”, Z. Naturfors. Sect. A-J. Phys. Sci., 73:6 (2018), 539–546  crossref  isi  scopus
    6. O. Bogoyavlenskij, “Invariants of the axisymmetric flows of an inviscid gas and fluid with variable density”, Z. Naturfors. Sect. A J. Phys. Sci., 73:10 (2018), 931–937  crossref  isi  scopus
    7. A. Enciso, M. Á. García-Ferrero, D. Peralta-Salas, “The Biot–Savart operator of a bounded domain”, J. Math. Pures Appl. (9), 119 (2018), 85–113  crossref  mathscinet  zmath  isi
    8. T. Machon, “The Godbillon-Vey invariant as a restricted Casimir of three-dimensional ideal fluids”, J. Phys. A-Math. Theor., 53:23 (2020), 235701  crossref  mathscinet  isi
    9. T. Machon, “The Godbillon-Vey invariant as topological vorticity compression and obstruction to steady flow in ideal fluids”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 476:2239 (2020), 20190851  crossref  mathscinet  isi
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