Geodesic
A solution class of the Euler equation in a torus with solenoidal velocity field. II
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 102-108 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study a problem on solutions $(\mathbf{V},p)$ of the Euler equation with solenoidal velocity field $\mathbf{V}$ in a torus $D$, which is similar to the problem considered in the authors' previous paper 2014. Now, the problem is considered in the class of vector fields $\mathbf{V}$ whose lines coincide with lines of latitude of tori embedded in $D$ with the same circular axis. Conditions are found under which this problem is solvable, and solutions are found too.
Keywords: scalar and vector fields, curl.
Mots-clés : Euler equation, divergence 
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V. P. Vereshchagin; Yu. N. Subbotin; N. I. Chernykh. A solution class of the Euler equation in a torus with solenoidal velocity field. II. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 102-108. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a9/

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[2] Vereschagin V.P., Subbotin Yu.N., Chernykh N.I., “K mekhanike vintovykh potokov v idealnoi neszhimaemoi nevyazkoi sploshnoi srede”, Tr. In-ta matematiki i mekhaniki UrO RAN, 18:4 (2012), 120–134

[3] Vereschagin V.P., Subbotin Yu.N., Chernykh N.I., “Postanovka i reshenie kraevoi zadachi v klasse ploskovintovykh vektornykh polei”, Tr. In-ta matematiki i mekhaniki UrO RAN, 18:1 (2012), 123–138 | MR

[4] Vereschagin V.P., Subbotin Yu.N., Chernykh N.I., “Nekotorye resheniya uravnenii dvizheniya dlya neszhimaemoi vyazkoi sploshnoi sredy”, Tr. In-ta matematiki i mekhaniki UrO RAN, 19:4 (2013), 48–63

[5] Vereschagin V.P., Subbotin Yu.N., Chernykh N.I., “Klass vsekh gladkikh edinichnykh aksialno simmetrichnykh vektornykh polei, prodolno vikhrevykh v R3”, Izv. Sarat. un-ta. Ser. “Matematika. Mekhanika. Informatika” 1., 9:4, ch. 1 (2009), 11–23