  We study the spatially inhomogeneous Landau equations with hard potential in
the perturbation setting, and establish the analytic smoothing effect in both
spatial and velocity variables for a class of low-regularity weak solutions.
This shows the Landau equations behave essentially as the hypoelliptic
Fokker-Planck operators. The spatial analyticity relies on a new time-average
operator, and the proof is based on a straightforward energy estimate with a
careful estimate on the derivatives with respect to the new time-average
operator.
