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

We find a general solution to the problem on the motion in an incompressible continuous medium occupying at any time a whole domain D ⊂ 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 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. © 2014 Pleiades Publishing, Ltd.Российский Фонд Фундаментальных Исследований (РФФИ): 12-01-0004, 11-01-00347, 11-01-00462Ministry of Education and Science of the Russian Federation: 1.5444.2011This work was supported by the Russian Foundation for Basic Research (project nos. 11-01-00462, 12-01-0004, and 11-01-00347) and by the Program for State Support of Leading Universities of the Russian Federation (agreement no. 02.A03.21.0006 of August 27, 2013). The research of the third author was also supported by the Ministry of Education and Science of the Russian Federation according to the state assignment to higher education institutions for carrying out fundamental and applied research (project no. 1.5444.2011)