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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2008, Volume 14, Number 3, Pages 82–91 (Mi timm42)  
This article is cited in 7 scientific papers (total in 8 papers)

On the construction of unit longitudinal-vortex vector fields with the use of smooth mappings

V. P. Vereshchagina, Yu. N. Subbotinb, N. I. Chernykhb

a Russian State Professional Pedagogical University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (263 kB) Citations (8)
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Abstract: A solution is given for the problem of constructing a unit vector field collinear to the field of its curl. The solution is based on the use of a suitably parametrized orthogonal transformation of a unit vector field that is potential in R3. The result is stated in the theorem that contains the recipe for constructing the required field.
Received: 20.03.2008
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, Volume 264, Issue 1, Pages S116–S125
DOI: https://doi.org/10.1134/S0081543809050095
Bibliographic databases:
Document Type: Article
UDC: 514.7
Language: Russian
Citation: V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “On the construction of unit longitudinal-vortex vector fields with the use of smooth mappings”, Trudy Inst. Mat. i Mekh. UrO RAN, 14, no. 3, 2008, 82–91; Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S116–S125
Citation in format AMSBIB
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\paper On the construction of unit longitudinal-vortex vector fields with the use of smooth mappings
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\vol 14
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\pages 82--91
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Linking options:
  • https://www.mathnet.ru/eng/timm42
  • https://www.mathnet.ru/eng/timm/v14/i3/p82
    • This publication is cited in the following 8 articles:
    1. Alexander Kuznetsov, Evgeny Shinder, “Derived categories of Fano threefolds and degenerations”, Invent. math., 2024  crossref
    2. Laura Pertusi, Paolo Stellari, “Categorical Torelli theorems: results and open problems”, Rend. Circ. Mat. Palermo, II. Ser, 72:5 (2023), 2949  crossref
    3. “Sovmestnaya nauchnaya deyatelnost Yu. N. Subbotina i N. I. Chernykh”, Tr. IMM UrO RAN, 17, no. 3, 2011, 4–7  mathnet
    4. “Yu. N. Subbotin and N. I. Chernykh's joint research activities”, Proc. Steklov Inst. Math. (Suppl.), 277:S1 (2012), –  mathnet  mathnet  crossref  isi  scopus
    5. V. P. Vereschagin, Yu. N. Subbotin, N. I. Chernykh, “K postroeniyu potentsialnykh i poperechno vikhrevykh vektornykh polei s liniyami nulevoi krivizny”, Tr. IMM UrO RAN, 16, no. 4, 2010, 117–127  mathnet  elib
    6. V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “Transformation that changes the geometric structure of a vector field”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S118–S128  mathnet  crossref  isi  elib
    7. V. P. Vereschagin, Yu. N. Subbotin, N. I. Chernykh, “Klass vsekh gladkikh edinichnykh aksialno simmetrichnykh vektornykh polei, prodolno vikhrevykh v $R^3$”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 9:4(1) (2009), 11–23  mathnet  crossref
    8. V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “Longitudinal-vortex unit vector fields from the class of axially symmetric fields”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S126–S132  mathnet  crossref  isi  elib
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