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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2009, Volume 9, Issue 4(1), Pages 11–23 (Mi isu70)  

This article is cited in 2 scientific papers (total in 3 papers)

Mathematics

The full class ofsmooth axially symmetric longitudinal-vortex unit vector fields

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

a Russian State Professional – Pedagogical University, Ekaterinburg
b Institute of Mathematics and Mechanics, Ural Branch of RAS, Ekaterinburg

Abstract: In the paper, two vector fields are constructed by means of transformation method. The first describes the axially symmetric unit solutions (ASUS) of the Gromeka problem to find out vector fields which flow lines coincide in $R^3$ with vortex lines. The second describes the smooth ASUS of the extended in this paper Gromeka problem of finding a vector fields with different vortex properties in adjacent parts of $R^3$.

Key words: scalar and vector fields, curl.

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UDC: 514.7

Citation: V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “The full class ofsmooth axially symmetric longitudinal-vortex unit vector fields”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 9:4(1) (2009), 11–23

Citation in format AMSBIB
\Bibitem{VerSubChe09}
\by V.~P.~Vereshchagin, Yu.~N.~Subbotin, N.~I.~Chernykh
\paper The full class ofsmooth axially symmetric longitudinal-vortex unit vector fields
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2009
\vol 9
\issue 4(1)
\pages 11--23
\mathnet{http://mi.mathnet.ru/isu70}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. “Sovmestnaya nauchnaya deyatelnost Yu. N. Subbotina i N. I. Chernykh”, Tr. IMM UrO RAN, 17, no. 3, 2011, 4–7  mathnet
    3. V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “A solution class of the Euler equation in a torus with solenoidal velocity field. II”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 236–242  mathnet  crossref  mathscinet  elib
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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