  We consider the spatially inhomogeneous Landau equation with initial data
that is bounded by a Gaussian in the velocity variable. In the case of
moderately soft potentials, we show that weak solutions immediately become
smooth and remain smooth as long as the mass, energy, and entropy densities
remain under control. For very soft potentials, we obtain the same conclusion
with the additional assumption that a sufficiently high moment of the solution
in the velocity variable remains bounded. Our proof relies on the iteration of
local Schauder-type estimates.
