  We construct bounded classical solutions of the Boltzmann equation in the
whole space without specifying any limit behaviors at the spatial infinity and
without assuming the smallness condition on initial data. More precisely, we
show that if the initial data is non-negative and belongs to a uniformly local
Sobolev space in the space variable with Maxwellian type decay property in the
velocity variable, then the Cauchy problem of the Boltzmann equation possesses
a unique non-negative local solution in the same function space, both for the
cutoff and non-cutoff collision cross section with mild singularity. The known
solutions such as solutions on the torus (space periodic solutions) and in the
vacuum (solutions vanishing at the spatial infinity), and solutions in the
whole space having a limit equilibrium state at the spatial infinity are
included in our category.
