Stability of the planar rarefaction wave to two-dimensional compressible Navier-Stokes equations

摘要

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