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We formulate a boundary value problem for the Navier–Stokes equations with prescribed u·n, curlu·n and alternatively (∂u/∂n)·n or curlu·n on the boundary. We deal with the question of existence of a steady weak solution. AMS Subject Classification: Primary: 35 Q 30; secondary: 76 D 05

The Navier–Stokes equation with inhomogeneous boundary conditions based on vorticity