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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 1, Pages 111–121 (Mi timm208)  

This article is cited in 6 scientific papers (total in 7 papers)

Transformation that changes the geometric structure of a vector field

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

Abstract: A method is proposed of constructing vector fields with certain vortex properties by means of transformations changing the value of the field vector at every point, the form of field lines, and their mutual position. We discuss and give concrete examples of the prospects of using the method in applications involving solution of partial differential equations, including nonlinear ones.

Keywords: vector fields, mutual orientation of a field and the field of its curl, mapping of vector fields

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 265, suppl. 1, S118–S128

Bibliographic databases:

UDC: 514.7
Received: 28.11.2008

Citation: V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “Transformation that changes the geometric structure of a vector field”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 1, 2009, 111–121; Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S118–S128

Citation in format AMSBIB
\by V.~P.~Vereshchagin, Yu.~N.~Subbotin, N.~I.~Chernykh
\paper Transformation that changes the geometric structure of a~vector field
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 1
\pages 111--121
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 265
\issue , suppl. 1
\pages S118--S128

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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “The class of solenoidal planar-helical vector fields”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S171–S187  mathnet  crossref  isi  elib
    4. “Sovmestnaya nauchnaya deyatelnost Yu. N. Subbotina i N. I. Chernykh”, Tr. IMM UrO RAN, 17, no. 3, 2011, 4–7  mathnet
    5. V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “On the mechanics of helical flows in an ideal incompressible viscous continuous medium”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 159–174  mathnet  crossref  isi  elib
    6. V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “Some solutions of continuum equations for an incompressible viscous fluid”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 208–223  mathnet  crossref  mathscinet  isi  elib
    7. V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “Description of a helical motion of an incompressible nonviscous fluid”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 202–210  mathnet  crossref  mathscinet  isi  elib
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