New efficient boundary conditions for incompressible Navier-Stokes equations: A well-posedness result

Efficient natural conditions on open boundaries for incompressible flows are derived from a weak formulation of Navier-Stokes equations. Energy estimates in velocity-pressure are established from a mixed formulation and a rigourous proof of existence of solutions is given. As an illustration, the conditions are written down for the flow behind an obstacle in a channel. Moreover, numerical tests have shown the accuracy and robustness of such conditions.