Two-dimensional inviscid channel flow of an incompressible fluid is considered. It is shown that if the flow is steady and features no horizontal stagnation, then the flow must necessarily be a parallel shear flow.

Application of the computer simulation for solving the incompressible flow problems motivates developing efficient and accurate numerical models. The set of Inviscid Incompressible Euler equations can be applied for wide range of engineering applications. For the steady state problems, the equation of continuity can be simultaneously solved with the equations of motion in a coupled manner using...

Given a stable configuration of point vortices for steady two-dimensional inviscid, incompressible fluid flow in a domain D, it is shown that there is another stable configuration of stationary vortices in D with vortices near the original vortices plus additional vortices near any points on the boundary where the speed of the original flow is a nonzero relative minimum.

We study linear and nonlinear instability of steady incompressible inviscid flows. First, some sufficient conditions of linear instability for a class of shear flows are given. Second, nonlinear instability in the L2-norm of velocity is proved under the assumption that the growth rate exceeds half of the Liapunov exponent of the steady flow, for any bounded domain. We also estimate the growth o...

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 phen...

We consider the flow of a viscous, incompressible, Newtonian fluid in a perforated domain in the plane. The domain is the exterior of a regular lattice of rigid particles. We study the simultaneous limit of vanishing particle size and distance, and of vanishing viscosity. Under suitable conditions on the particle size, particle distance, and viscosity, we prove that solutions of the Navier-Stok...

Statement of problem on vortical inviscid flow of barotropic and incompressible fluids. Abstract The question what information is necessary for determination of a unique solution of hydrodynamic equations for ideal fluid is investigated. Arbitrary inviscid flows of the barotropic fluid and of incompressible fluid are considered. After integrating hydrodynamic equations, all information on the f...