  We present the first results of our spatially axisymmetric core-collapse
supernova simulations with full Boltzmann neutrino transport, which amount to a
time-dependent 5-dimensional (2 in space and 3 in momentum space) problem in
fact. Special relativistic effects are fully taken into account with a
two-energy-grid technique. We performed two simulations for a progenitor of
11.2M, employing different nuclear equations-of-state (EOS's): Lattimer and
Swesty's EOS with the incompressibility of K = 220MeV (LS EOS) and Furusawa's
EOS based on the relativistic mean field theory with the TM1 parameter set (FS
EOS). In the LS EOS the shock wave reaches ~700km at 300ms after bounce and is
still expanding whereas in the FS EOS it stalled at ~200km and has started to
recede by the same time. This seems to be due to more vigorous turbulent
motions in the former during the entire post-bounce phase, which leads to
higher neutrino-heating efficiency in the neutrino-driven convection. We also
look into the neutrino distributions in momentum space, which is the advantage
of the Boltzmann transport over other approximate methods. We find
non-axisymmetric angular distributions with respect to the local radial
direction, which also generate off-diagonal components of the Eddington tensor.
We find that the r {\theta}-component reaches ~10% of the dominant rr-component
and, more importantly, it dictates the evolution of lateral neutrino fluxes,
dominating over the {\theta}{\theta}-component, in the semi-transparent region.
These data will be useful to further test and possibly improve the
prescriptions used in the approximate methods.
