Non-linear asymptotic stability for the through-passing flows of inviscid incompressible fluid

The paper addresses the dynamics of inviscid incompressible fluid confined within bounded domain with the inflow and outflow of fluid through certain parts of the boundary. This system is non-conservative essentially since the fluxes of energy and vorticity through the flow boundary are not equal to zero. Therefore, the dynamics of such flows should demonstrate the generic non-conservative phenomena such as the asymptotic stability of the equilibria, the onset of instability or the excitation of the self-oscillations, etc. These phenomena are studied extensively for the flows of the viscous fluids but not for the inviscid ones. In this paper, we prove a sufficient condition for the non-linear asymptotic stability of the inviscid steady flows.