Vanishing dissipation limit of planar wave patterns to the multi-dimensional compressible Navier-Stokes equations

The talk is concerned with our recent results on the vanishing viscosities limit of planar rarefaction wave to both 2D compressible isentropic Navier-Stokes equations and 3D full compressible Navier-Stokes equations and the vanishing dissipation limit of planar contact discontinuity to 3D full compressible Navier-Stokes equations. Remark that the planar shock wave is non-unique and the planar rarefaction wave is unique in the class of entropic solutions to 3D compressible Euler equations and whether the planar contact discontinuity is unique or not for entropic weak solutions is still open to 3D compressible Euler equations. And our vanishing dissipation limit for planar contact discontinuity, in particular, impies the positive answer to the uniqueness of a planar contact discontinuity for 3D compressible Euler equations in the class of zero dissipation limit of full compressible Navier-Stokes equations.