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 Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 2, Pages 91–100 (Mi timm1294)

A solution class of the Euler equation in a torus with solenoidal velocity field. III

V. P. Vereshchagin, Yu. N. Subbotinab, N. I. Chernykhab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: We continue the study of the problem on the existence conditions for solenoidal solutions of the Euler equation in a torus $D$ with respect to a pair $(\mathbf{V},p)$ of vector and scalar fields such that the lines of the vector field $\mathbf{V}$ have a simple structure, coinciding with parallels and meridians of toroidal surfaces that are concentrically embedded in $D$. Here, in contrast to the previous two papers, the right-hand side of the Euler equation, i.e., the vector field $\mathbf{f}$ in $D$, is not given in a special form but is considered to be arbitrary.

Keywords: scalar and vector fields, Euler equation, divergence, curl.

 Funding Agency Grant Number Russian Science Foundation 14-11-00702

DOI: https://doi.org/10.21538/0134-4889-2016-22-2-91-100

Full text: PDF file (188 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 514.17; 532.5
MSC: 35Q30, 35Q31, 76D07, 76N10

Citation: V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “A solution class of the Euler equation in a torus with solenoidal velocity field. III”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 2, 2016, 91–100

Citation in format AMSBIB
\Bibitem{VerSubChe16} \by V.~P.~Vereshchagin, Yu.~N.~Subbotin, N.~I.~Chernykh \paper A solution class of the Euler equation in a torus with solenoidal velocity field. III \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2016 \vol 22 \issue 2 \pages 91--100 \mathnet{http://mi.mathnet.ru/timm1294} \crossref{https://doi.org/10.21538/0134-4889-2016-22-2-91-100} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3559165} \elib{https://elibrary.ru/item.asp?id=26040819}