The limit of the boltzmann equation to the euler equations for riemann problems

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1741-1811
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume45
Issue number3
Online published13 Jun 2013
Publication statusPublished - 2013

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Abstract

The convergence of the Boltzmann equation to the compressible Euler equations when the Knudsen number tends to zero has been a long-standing open problem in kinetic theory. In the setting of a Riemann solution that contains the generic superposition of shock, rarefaction wave, and contact discontinuity to the Euler equations, we succeed in justifying this limit by introducing hyperbolic waves with different solution backgrounds to capture the extra masses carried by the hyperbolic approximation of the rarefaction wave and the diffusion approximation of contact discontinuity. © 2013 Society for Industrial and Applied Mathematics.

Research Area(s)

  • Boltzmann equation, Euler equations, Hydrodynamic limit, Riemann solution

Citation Format(s)

The limit of the boltzmann equation to the euler equations for riemann problems. / Huang, Feimin; Wang, Yi; Wang, Yong et al.
In: SIAM Journal on Mathematical Analysis, Vol. 45, No. 3, 2013, p. 1741-1811.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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