Geodesic
Transformation that changes the geometric structure of a vector field
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 111-121
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@article{TIMM_2009_15_1_a8,
     author = {V. P. Vereshchagin and Yu. N. Subbotin and N. I. Chernykh},
     title = {Transformation that changes the geometric structure of a~vector field},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {111--121},
     year = {2009},
     volume = {15},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a8/}
}
TY  - JOUR
AU  - V. P. Vereshchagin
AU  - Yu. N. Subbotin
AU  - N. I. Chernykh
TI  - Transformation that changes the geometric structure of a vector field
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2009
SP  - 111
EP  - 121
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a8/
LA  - ru
ID  - TIMM_2009_15_1_a8
ER  - 
%0 Journal Article
%A V. P. Vereshchagin
%A Yu. N. Subbotin
%A N. I. Chernykh
%T Transformation that changes the geometric structure of a vector field
%J Trudy Instituta matematiki i mehaniki
%D 2009
%P 111-121
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a8/
%G ru
%F TIMM_2009_15_1_a8
V. P. Vereshchagin; Yu. N. Subbotin; N. I. Chernykh. Transformation that changes the geometric structure of a vector field. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 111-121. http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a8/

[1] Craig Th., “On certain possible cases of steady motion in a viscous fluid”, Amer. J. Math., 3:3 (1880), 269–288 | DOI | MR

[2] Gromeka I. S., Sobranie sochinenii, Izd-vo AN SSSR, M., 1952, 296 pp. | MR

[3] Beltrami E., “Considerazioni idrodinamiche”, Rend. Istit. Lombardo Accad. Sci. Lett., 22 (1889), 121–130

[4] Korn G., Korn T., Spravochnik po matematike (dlya nauchnykh rabotnikov i inzhenerov), Nauka, M., 1977, 832 pp. | MR

[5] Aminov Yu. A., Geometriya vektornogo polya, Nauka, M., 1990, 208 pp. | MR

[6] Vereschagin V. P., Subbotin Yu. N., Chernykh N..I., “K postroeniyu edinichnykh prodolno vikhrevykh vektornykh polei s pomoschyu gladkikh otobrazhenii”, Tr. In-ta matematiki i mekhaniki UrO RAN, 14, no. 3, 2008, 82–91

[7] Vereschagin V. P., Subbotin Yu. N., Chernykh N. I., “Prodolno vikhrevye edinichnye vektornye polya iz klassa aksialno simmetrichnykh polei”, Tr. In-ta matematiki i mekhaniki UrO RAN, 14, no. 3, 2008, 92–98