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Non-Local Scattering Kernel and the Hydrodynamic Limit

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In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier–Stokes equations.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Palermo, Via Archirafi 34, 90123, Palermo, Italy

    Maria Carmela Lombardo & Marco Sammartino

  2. Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, CA, 90095, USA

    Russel E. Caflisch

Authors
  1. Maria Carmela Lombardo
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  2. Russel E. Caflisch
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  3. Marco Sammartino
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Correspondence to Maria Carmela Lombardo.

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Lombardo, M.C., Caflisch, R.E. & Sammartino, M. Non-Local Scattering Kernel and the Hydrodynamic Limit. J Stat Phys 130, 69–82 (2008). https://doi.org/10.1007/s10955-007-9360-7

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  • DOI: https://doi.org/10.1007/s10955-007-9360-7

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