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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)685-728
Journal / PublicationKinetic and Related Models
Issue number4
Publication statusPublished - Dec 2010


Fluid dynamic limit to compressible Euler equations from com-pressible Navier-Stokes equations and Boltzmann equation has been an active topic with limited success so far. In this paper, we consider the case when the solution of the Euler equations is a Riemann solution consisting two rarefaction waves and a contact discontinuity and prove this limit for both Navier-Stokes equations and the Boltzmann equation when the viscosity, heat conductivity coefficients and the Knudsen number tend to zero respectively. In addition, the uniform convergence rates in terms of the above physical parameters are also obtained. It is noted that this is the first rigorous proof of this limit for a Riemann solution with superposition of three waves even though the fluid dynamic limit for a single wave has been proved. © American Institute of Mathematical Sciences.

Research Area(s)

  • Boltzmann equation, Compressible Navier-Stokes equations, Contact discontinuity, Fluid dynamic limit, Rarefaction wave