Geodesic
On the mechanics of helical flows in an ideal incompressible viscous continuous medium
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 120-134

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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
Mots-clés : Euler equation, Gromeka's problem. 
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     title = {On the mechanics of helical flows in an ideal incompressible viscous continuous medium},
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V. P. Vereshchagin; Yu. N. Subbotin; N. I. Chernykh. On the mechanics of helical flows in an ideal incompressible viscous continuous medium. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 120-134. http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a10/