Variational principles and stability of the inviscid open flows

In this article, we study the stability of the steady solutions of boundary value problems for ideal incompressible fluid flows through a given domain. For doing this we generalize Arnold's form of the direct Liapunov method (1966) that was being applied earlier to the cases of fully impermeable boundaries or periodic flows only. We ascertain a number of criteria for Liapunov stability or asymptotic stability as well as new classes of open flows possessing the mentioned properties. In addition, we prove that the occurrence of the recirculation areas is inevitable in rather wide classes of open channel flows.