Asymptotic behavior of small perturbations for unsteady motion an ideal fluid jet

The stability problem of unsteady rotating circular jet motion of an ideal fluid is reduced to solving an initial-boundary value problem for Poincare–Sobolev type equation with an evolutionary condition on the jet free initial boundary. The solution of this problem is constructed by the method of variables separation. The asymptotic amplitudes behavior perturbations of the free jet boundary at $ t \rightarrow \infty $ is found. The results obtained are compared with the known results on the stability of the potential jet motion.