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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 4, Pages 60–70 (Mi timm1115)  
This article is cited in 2 scientific papers (total in 2 papers)

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

V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (183 kB) Citations (2)
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Abstract: A system of equations with respect to a pair $(\mathbf V,p)$ 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 $\mathbf f$ and the solenoidality equation for the field $\mathbf V$. We seek for solutions $(\mathbf V,p)$ of this system for which lines of the vector field $\mathbf V$ inside $D$ coincide with meridians of tori embedded in $D$ with the same circular axis. Conditions on the vector field $\mathbf f$ under which the problem is solvable are established, and the whole class of such solutions is described.
Keywords: scalar and vector fields, Euler equation, divergence, curl.
Received: 18.08.2014
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, Volume 288, Issue 1, Pages 211–221
DOI: https://doi.org/10.1134/S0081543815020224
Bibliographic databases:
Document Type: Article
UDC: 514.17+532.5
Language: Russian
Citation: V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “A solution class of the Euler equation in a torus with solenoidal velocity field”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 4, 2014, 60–70; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 211–221
Citation in format AMSBIB
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\paper A solution class of the Euler equation in a~torus with solenoidal velocity field
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\yr 2014
\vol 20
\issue 4
\pages 60--70
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\vol 288
\issue , suppl. 1
\pages 211--221
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