  We present a stability analysis for two different rotational pressure
correction schemes with open and traction boundary conditions. First, we
provide a stability analysis for a rotational version of the grad-div
stabilized scheme of [A. Bonito, J.-L. Guermond, and S. Lee. Modified
pressure-correction projection methods: Open boundary and variable time
stepping. In Numerical Mathematics and Advanced Applications - ENUMATH 2013,
volume 103 of Lecture Notes in Computational Science and Engineering, pages
623-631. Springer, 2015]. This scheme turns out to be unconditionally stable,
provided the stabilization parameter is suitably chosen. We also establish a
conditional stability result for the boundary correction scheme presented in
[E. Bansch. A finite element pressure correction scheme for the Navier-Stokes
equations with traction boundary condition. Comput. Methods Appl. Mech. Engrg.,
279:198-211, 2014]. These results are shown by employing the equivalence
between stabilized gauge Uzawa methods and rotational pressure correction
schemes with traction boundary conditions.

Numerical Analysis