On the Stokes problem with model boundary conditions

For a wide class of two- and three-dimensional domains, boundary conditions on the velocity vector field for the Stokes problem are indicated ensuring that the corresponding Schur complement is the identity operator. These boundary conditions make it possible to “decouple” the Stokes problem into two separate problems, for pressure and for velocity. The solubility of the problem and the regularity of its solutions are studied and the connections between the results obtained and certain aspects of numerical methods in hydrodynamics (such as the LBB condition and the numerical solution of the generalized Stokes problem) are considered.