V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “On the mechanics of helical flows in an ideal incompressible viscous continuous medium”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 4, 2012, 120–134; Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 159

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Volume 18, Number 4, Pages 120–134 (Mi timm872)

This article is cited in 7 scientific papers (total in 7 papers)

On the mechanics of helical flows in an ideal incompressible viscous continuous medium

V. P. Vereshchagin^a, Yu. N. Subbotin^bc, N. I. Chernykh^cb

^a Russian State Professional Pedagogical University, Ekaterinburg
^b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
^c Institute of Mathematics and Computer Science, Ural Federal University

Full-text PDF (214 kB) Citations (7)

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Abstract: We find a general solution to the problem on the motion in an incompressible continuous medium occupying at any time a whole domain $D\subset R^3$ under the conditions that $D$ is an axially symmetric cylinder and the motion is described by the Euler equation together with the continuity equation for an incompressible medium and belongs to the class of planar-helical flows (according to I. S. Gromeka's terminology), in which sreamlines coincide with vortex lines. This class is constructed by the method of transformation of the geometric structure of a vector field. The solution is characterized in Theorem 2 in the end of the paper.

Keywords: scalar fields, vector fields, tensor fields, curl, Euler equation, Gromeka's problem.

Received: 23.07.2012

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 284, Issue 1, Pages 159–174
DOI: https://doi.org/10.1134/S008154381402014X

Bibliographic databases:

Document Type: Article

UDC: 514.17+532.5

Language: Russian

Citation: V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “On the mechanics of helical flows in an ideal incompressible viscous continuous medium”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 4, 2012, 120–134; Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 159–174

Citation in format AMSBIB

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https://www.mathnet.ru/eng/timm/v18/i4/p120

This publication is cited in the following 7 articles:

G. B. Sizykh, “Rasscheplenie uravnenii Nave–Stoksa dlya odnogo klassa osesimmetrichnykh techenii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 24:1 (2020), 163–173
G. B. Sizykh, “Axisymmetric helical flow of viscous fluid”, Russian Math. (Iz. VUZ), 63:2 (2019), 44–50
V. P. Vereschagin, Yu. N. Subbotin, N. I. Chernykh, “Odin klass reshenii uravneniya Eilera v tore s solenoidalnym polem skorostei. III”, Tr. IMM UrO RAN, 22, no. 2, 2016, 91–100
V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “A solution class of the Euler equation in a torus with solenoidal velocity field. II”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 236–242
V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “Description of a helical motion of an incompressible nonviscous fluid”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 202–210
V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “A solution class of the Euler equation in a torus with solenoidal velocity field”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 211–221
V. P. Vereshchagin, Yu. N. Subbotin, N. I. Chernykh, “Some solutions of continuum equations for an incompressible viscous fluid”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 208–223

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Instituta Matematiki i Mekhaniki UrO RAN

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