The Class of Solenoidal Planar-Helical Vector Fields / Vereshchagin V. P.,Subbotin Yu. N.,Chernykh N. I. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2011. - V. 273, l. 1. - P. S171-S187.

ISSN/EISSN:

0081-5438 / нет данных

Type:

Article

Abstract:

The class of solenoidal vector fields whose lines lie in planes parallel to R-2 is constructed by the method of mappings. This class exhausts the set of all smooth planarhelical solutions of Gromeka's problem in some domain D subset of R-3. In the case of domains D with cylindrical boundaries whose generators are orthogonal to R-2, it is shown that the choice of a specific solution from the constructed class is reduced to the Dirichlet problem with respect to two functions that are harmonic conjugates in D-2 = D boolean AND R-2; i. e., Gromeka's nonlinear problem is reduced to linear boundary value problems. As an example, a specific solution of the problem for an axisymmetric layer is presented. The solution is based on solving Dirichlet problems in the form of series uniformly convergent in (D) over bar (2) in terms of wavelet systems that form bases of various spaces of functions harmonic in D-2.

Author keywords:

scalar fields; vector fields; tensor fields; curl; wavelets; Gromeka's problem

DOI:

10.1134/S008154381105018X

Web of Science ID:

ISI:000305481300018

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	JUL
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
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 {[}09-01-00014]; Ural Branch of the Russian Academy of Sciences under the Program of the Presidium of the Russian Academy of Sciences ``Mathematical Theory of Control{''}
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project no. 09-01-00014) and by the Ural Branch of the Russian Academy of Sciences under the Program of the Presidium of the Russian Academy of Sciences ``Mathematical Theory of Control.{''}
Number-of-Cited-References	8
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	961QG