  In this paper we are concerned with the steady Navier-Stokes and Stokes
problems with mixed boundary conditions involving Tresca slip, leak condition,
one-sided leak conditions, velocity, pressure, rotation, stress and normal
derivative of velocity together. Relying on the relations among strain,
rotation, normal derivative of velocity and shape of boundary surface, we have
variational formulations for the problems, which consist of five formulae with
five unknowns. We get the variational inequalities equivalent to the formulated
variational problems, which have one unknown. Then, we study the corresponding
variational inequalities and relying the results for variational inequalities,
we get existence, uniqueness and estimates of solutions to the Navier-Stokes
and Stokes problems with the boundary conditions. Our estimates for solutions
do not depend on the thresholds for slip and leaks.
