Stability of planar rarefaction wave to 3D full compressible Navier-Stokes equations

Abstract

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.