Description of a Helical Motion of an Incompressible Nonviscous Fluid / Vereshchagin V. P.,Subbotin Yu. N.,Chernykh N. I. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2015. - V. 288, l. 1. - P. S202-S210.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

We consider the problem of describing the motion of a fluid filling at any specific time t >= 0 a domain D subset of R-3 in terms of velocity v and pressure p. We assume that the pair of variables (v, p) satisfies a system of equations that includes Euler's equation and the incompressible fluid continuity equation. For the case of an axially symmetric cylindrical layer D, we find a general solution of this system of equations in the class of vector fields v whose lines for any t >= 0 coincide everywhere in D with their vortex lines and lie on axially symmetric cylindrical surfaces nested in D. The general solution is characterized in a theorem. As an example, we specify a family of solutions expressed in terms of cylindrical functions, which, for D = R-3, includes a particular solution obtained for the first time by I.S. Gromeka in the case of steady-state helical cylindrical motions.

Author keywords:

scalar and vector fields; curl; helical motion; Gromeka's problem

DOI:

10.1134/S0081543815020212

Web of Science ID:

ISI:000352991400020

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 Nikolai.Chernykh@imm.uran.ru
ResearcherID-Numbers	Subbotin, Yurii Nikolaevich/C-4273-2017
Funding-Acknowledgement	Russian Foundation for Basic Research {[}11-01-00462, 12-01-00004, 14-01-00496]; Ministry of Education and Science of the Russian Federation {[}1.5444.2011]; Program for State Support of Leading Universities of the Russian Federation {[}02.A03.21.0006]; Russian President's Grant for State Support of Leading Scientific Schools {[}NSh-4538.2014.1]
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project nos. 11-01-00462, 12-01-00004, and 14-01-00496), by the Ministry of Education and Science of the Russian Federation (project no. 1.5444.2011), by the Program for State Support of Leading Universities of the Russian Federation (agreement no. 02.A03.21.0006 of August 27, 2013), and by the Russian President's Grant for State Support of Leading Scientific Schools (project no. NSh-4538.2014.1).
Number-of-Cited-References	4
Usage-Count-Last-180-days	2
Usage-Count-Since-2013	10
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	CG0VY