  This article considers the spatially inhomogeneous, non-cutoff Boltzmann
equation. We construct a large-data classical solution given bounded,
measurable initial data with uniform polynomial decay of mild order in the
velocity variable. Our result requires no assumption of strict positivity for
the initial data, except locally in some small ball in phase space. We also
obtain existence results for weak solutions when our decay and positivity
assumptions for the initial data are relaxed. Because the regularity of our
solutions may degenerate as $t \rightarrow 0$, uniqueness is a challenging
issue. We establish weak-strong uniqueness under the additional assumption that
the initial data possesses no vacuum regions and is H\"older continuous. As an
application of our short-time existence theorem, we prove global existence near
equilibrium for bounded, measurable initial data that decays at a finite
polynomial rate in velocity.
