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On the limit of the nonlinear Enskog equation corresponding with fluid dynamics

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Abstract

We prove that if a scale of the diameter of particles is not greater than a scale of the mean free path to a high enough power, if the scale of the mean free path is sufficiently small, and if the non-hydrodynamic part of the initial data satisfies an assumption of smallness, then a solution of the initial-value problem exists for the Enskog equation on a macroscopic time interval as long as a smooth solution of the Euler equations for compressible fluids exists. This Enskog solution is approximated both by the corresponding solution of the Boltzmann equation and by the solution of the Euler equations.

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Authors and Affiliations

  1. Istituto Matematico “Guido Castelnuovo”, Università di Roma, Italy

    Mirosław Lachowicz

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  1. Mirosław Lachowicz
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Communicated by L. Arkeryd

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Lachowicz, M. On the limit of the nonlinear Enskog equation corresponding with fluid dynamics. Arch. Rational Mech. Anal. 101, 179–194 (1988). https://doi.org/10.1007/BF00251460

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  • DOI: https://doi.org/10.1007/BF00251460

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