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Efficient natural condition s 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.

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