Fluid dynamic limit to the Riemann Solutions of Euler equations: I. Superposition of rarefaction waves and contact discontinuity

Fluid dynamic limit to compressible Euler equationsfrom compressible Navier-Stokes equations and Boltzmann equation hasbeen an active topic with limited success so far. In this paper,we consider the case when the solution of the Euler equations is aRiemann solution consisting two rarefaction waves and a contactdiscontinuity and prove this limit for both Navier-Stokes equationsand the Boltzmann equation when the viscosity, heat conductivitycoefficients and the Knudsen number tend to zero respectively. Inaddition, the uniform convergence rates in terms of the abovephysical parameters are also obtained. It is noted that this is thefirst rigorous proof of this limit for a Riemann solution withsuperposition of three waves even though the fluid dynamic limit fora single wave has been proved.