  We investigate the time-asymptotic stability of planar rarefaction wave for
the three-dimensional Boltzmann equation, based on the micro-macro
decomposition introduced in [24, 22] and our new observations on the underlying
wave structures of the equation to overcome the difficulties due to the wave
propagation along the transverse directions and its interactions with the
planar rarefaction wave. Note that this is the first stability result of planar
rarefaction wave for 3D Boltzmann equation, while the corresponding results for
the shock and contact discontinuities are still completely open.
