  It is well-known that the rarefaction wave, one of the basic wave patterns to
the hyperbolic conservation laws, is nonlinearly stable to the one-dimensional
compressible Navier-Stokes equations (cf. [14,15,12,17]). In the present paper
we proved the time-asymptotically nonlinear stability of the planar rarefaction
wave to the two-dimensional compressible and isentropic Navier-Stokes
equations, which gives the first stability result of the planar rarefaction
wave to the multi-dimensional system with physical viscosities.
