Solvability of the initial boundary-value problems for hyperbolic model of ideal incompressible liquid motion

We consider rotationally-symmetrical solutions to Euler equations with a linear dependence of axial component of velocity on axial coordinate. By methods of group analysis of differential equations these equations were reduced to one hyperbolic equation of the fourth order. For this equation a local in time unique solvability of initial boundary-value problem was proved. Also, for this equation a generalized Goursat problem was considered. There were formulated sufficient conditions of its solution non-existence and conditions of classical solution existence in case it is defined for all values of the radial coordinate. It is established that in the class of considered solutions to Euler equations, setting up initial velocity field in whole space does not determine the solution to Cauchy problem uniquely.