A Solution Class of the Euler Equation in a Torus with Solenoidal Velocity Field / Vereshchagin V. P.,Subbotin Yu. N.,Chernykh N. I. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2015. - V. 288, l. 1. - P. S211-S221.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

A system of equations with respect to a pair (V, p) of a scalar field and a vector field in a torus D is considered. The system consists of the Euler equation with a given vector field f and the solenoidality equation for the field V. We seek for solutions (V, p) of this system such that the lines of the vector field V inside D coincide with meridians of tori embedded in D with the same circular axis. Conditions on the vector field f under which the problem is solvable are established, and the whole class of such solutions is described.

Author keywords:

scalar and vector fields; Euler equation; divergence; curl

DOI:

10.1134/S0081543815020224

Web of Science ID:

ISI:000352991400021

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 Science Foundation {[}14-11-00702]
Funding-Text	This work was supported by the Russian Science Foundation (project no. 14-11-00702).
Number-of-Cited-References	4
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	CG0VY