  This paper analyzes a class of globally divergence-free (and therefore
pressure-robust) hybridizable discontinuous Galerkin (HDG) finite element
methods for stationary Navier-Stokes equations. The methods use the
$\mathcal{P}_{k}/\mathcal{P}_{k-1}$ $(k\geq1)$ discontinuous finite element
combination for the velocity and pressure approximations in the interior of
elements, and piecewise $\mathcal{P}_k/\mathcal{P}_{k}$ for the trace
approximations of the velocity and pressure on the inter-element boundaries. It
is shown that the uniqueness condition for the discrete solution is guaranteed
by that for the continuous solution together with a sufficiently small mesh
size. Based on the derived discrete HDG Sobolev embedding properties, optimal
error estimates are obtained. Numerical experiments are performed to verify the
theoretical analysis.
