The approximation of a nonstandard Stokes problem using spectral methods is discussed in this paper. In this problem, in addition to the pressure being assigned on a part of the boundary, the tangential vorticity is given, on another part of the boundary.

Several spectral discretizations are proposed and analyzed. The inf-sup conditions, associated with the discretizations of this problem, and with the spurious modes that follow from them, are thoroughly studied.

The proofs of the theorems are clearly presented. The paper is well organized. The contribution of the paper is important, and should be useful to others working in this area.