Nonstationary cylindrical vortex in an ideal fluid

Equations of rotationally symmetric motion of an ideal incompressible fluid are considered. A class of solutions to these equations, described by a hyperbolic equation of the fourth order with one space variable, for which an initial boundary-value problem is formulated, is distinguished. The new class of exact solutions of the Euler equations was used to describe the a nonstationary cylindrical vortex in an ideal fluid.