  We prove the time-asymptotic stability toward planar rarefaction wave for the
three-dimensional full compressible Navier-Stokes equations in an infinite long
flat nozzle domain $\mathbb{R}\times\mathbb{T}^2$. Compared with
one-dimensional case, the proof here is based on our new observations on the
cancellations on the flux terms and viscous terms due to the underlying wave
structures, which are crucial to overcome the difficulties due to the wave
propagation along the transverse directions $x_2$ and $x_3$ and its
interactions with the planar rarefaction wave in $x_1$ direction.
