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Moment Systems Derived from Relativistic Kinetic Equations

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Abstract

In this paper, we are interested in the derivation of macroscopic equations from kinetic ones using a moment method in a relativistic framework. More precisely, we establish the general form of moments that are compatible with the Lorentz invariance and derive a hierarchy of relativistic moment systems from a Boltzmann kinetic equation. The proof is based on the representation theory of Lie algebras. We then extend this derivation to the classical case and general families of moments that obey the Galilean invariance are also constructed. It is remarkable that the set of formal classical limits of the so-obtained relativistic moment systems is not identical to the set of classical moments quoted in Ref. 21 and one could use a new physically relevant criterion to derive suitable moment systems in the classical case. Finally, the ultra-relativistic limit is considered.

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Authors and Affiliations

  1. Mathématiques pour l’Industrie et la Physique, CNRS UMR 5640, Université Paul Sabatier-Toulouse 3, 118 route de Narbonne, F-31062, Toulouse cedex 9, France

    Véronique Bagland, Pierre Degond & Mohammed Lemou

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  1. Véronique Bagland
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  2. Pierre Degond
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  3. Mohammed Lemou
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Correspondence to Véronique Bagland.

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Bagland, V., Degond, P. & Lemou, M. Moment Systems Derived from Relativistic Kinetic Equations. J Stat Phys 125, 621–659 (2006). https://doi.org/10.1007/s10955-006-9173-0

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