  For smooth domains, Liu et al. (Comm. Pure Appl. Math. 60: 1443-1487, 2007)
used optimal estimates for the commutator of the Laplacian and the Leray
projection operator to establish well-posedness of an extended Navier-Stokes
dynamics. In their work, the pressure is not determined by incompressibility,
but rather by a certain formula involving the Laplace-Leray commutator. A key
estimate of Liu et al. controls the commutator strictly by the Laplacian in
energy norm at leading order. In this paper we show that this strict control
fails in a large family of bounded planar domains with corners. However, when
the domain is an infinite cone, we find that strict control may be recovered in
certain power-law weighted norms.
