  We present analysis of two lowest-order hybridizable discontinuous Galerkin
methods for the Stokes problem, while making only minimal regularity
assumptions on the exact solution. The methods under consideration have
previously been shown to produce $H(\textrm{div})$-conforming and
divergence-free approximate velocities. Using these properties, we derive a
priori error estimates for the velocity that are independent of the pressure.
These error estimates, which assume only $H^{1+s}$-regularity of the exact
velocity fields for any $s \in [0, 1]$, are optimal in a discrete energy norm.
Error estimates for the velocity and pressure in the $L^2$-norm are also
derived in this minimal regularity setting. Our theoretical findings are
supported by numerical computations.
