  This paper establishes global weighted Calder\'on-Zygmund type regularity
estimates for weak solutions of a class of generalized Stokes systems in
divergence form. The focus of the paper is on the case that the coefficients in
the divergence-form Stokes operator consist of symmetric and skew-symmetric
parts, which are both discontinuous. Moreover, the skew-symmetric part is not
required to be bounded and therefore it could be singular. Sufficient
conditions on the coefficients are provided to ensure the global weighted
$W^{1,p}$-regularity estimates for weak solutions of the systems. As a direct
application, we show that our $W^{1,p}$-regularity results give some criteria
in critical spaces for the global regularity of weak Leray-Hopf solutions of
the Navier-Stokes system of equation
