On the Mechanics of Helical Flows in an Ideal Incompressible Nonviscous Continuous Medium / Vereshchagin V. P.,Subbotin Yu N.,Chernykh N. I. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2014. - V. 284, l. 1. - P. S159-S174.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

We find a general solution to the problem on the motion in an incompressible continuous medium occupying at any time a whole domain D subset of R-3 under the conditions that D is an axially symmetric cylinder and the motion is described by the Euler equation together with the continuity equation for an incompressible medium and belongs to the class of helical flows (according to I.S. Gromeka's terminology), in which sreamlines coincide with vortex lines. This class is constructed by the method of transformation of the geometric structure of a vector field. The solution is characterized in Theorem 2 in the end of the paper.

Author keywords:

scalar fields; vector fields; tensor fields; curl; Euler equation; Gromeka's problem.

DOI:

10.1134/S008154381402014X

Web of Science ID:

ISI:000334277400014

Соавторы в МНС:

Другие поля

Поле	Значение
Month	APR
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8605
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	yunsub@imm.uran.ru Chernykh@imm.uran.ru
ResearcherID-Numbers	Subbotin, Yurii Nikolaevich/C-4273-2017
Funding-Acknowledgement	Russian Foundation for Basic Research {[}11-01-00462, 12-01-0004, 11-01-00347]; Program for State Support of Leading Universities of the Russian Federation {[}02.A03.21.0006]; Ministry of Education and Science of the Russian Federation {[}1.5444.2011]
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project nos. 11-01-00462, 12-01-0004, and 11-01-00347) and by the Program for State Support of Leading Universities of the Russian Federation (agreement no. 02.A03.21.0006 of August 27, 2013). The research of the third author was also supported by the Ministry of Education and Science of the Russian Federation according to the state assignment to higher education institutions for carrying out fundamental and applied research (project no. 1.5444.2011).
Number-of-Cited-References	8
Usage-Count-Last-180-days	1
Usage-Count-Since-2013	14
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	AE8UG