New steady and self-similar solutions of the Euler equations

Exact steady and self-similar solutions of the Euler equations are considered, which possess the property of partial invariance with respect to a certain six-parameter Lie group. New examples of vortex motion of a swirled liquid in curved channels are presented. A classification is given for self-similar solutions of the reduced system with two independent variables, which admits a three-parameter group of extensions, whereas the initial system of the Euler equations possesses a two-parameter group.