RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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
Received: 04.02.2016

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}


Linking options:
  • http://mi.mathnet.ru/eng/timm1294
  • http://mi.mathnet.ru/eng/timm/v22/i2/p91

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Number of views:
    This page:137
    Full text:36
    References:20
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021