Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Vereshchagin V. П., Subbotin Y. Н., Chernyh N. И. The Full Class of Smooth Axially Symmetric Longitudinal-Vortex Unit Vector Fields. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2009, vol. 9, iss. 4, pp. 11-23. DOI: 10.18500/1816-9791-2009-9-4-1-11-23

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
23.11.2009
Full text:
(downloads: 178)
Language: 
Russian
Heading: 
UDC: 
514.7

The Full Class of Smooth Axially Symmetric Longitudinal-Vortex Unit Vector Fields

Autors: 
Vereshchagin V.P. П., Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Subbotin Y.N. Николаевич, Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Chernyh N.I. И., Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
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 R3 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 R3.

References: 
  1. Верещагин В.П., Субботин Ю.Н., Черных Н.И. К построению единичных продольно вихревых векторных полей с помощью гладких отображений // Тр. Ин-та математики и механики УрО РАН. 2008. Т. 14, № 3. C. 82–91.
  2. Верещагин В.П., Субботин Ю.Н., Черных Н.И. Продольно вихревые единичные векторные поля из класса аксиально симметричных полей // Тр. Ин-та математики и механики УрО РАН. 2008. Т. 14, № 3. C. 92–98.
  3. Громека И.С. Собрание сочинений. М.: Из-во АН СССР, 1952. 296 с.
  4. Верещагин В.П., Субботин Ю.Н., Черных Н.И. Преобразование, изменяющее геометрическое строение векторного поля // Тр. Ин-та математики и