Non-local scattering kernel and the hydrodynamic limit

Maria Carmela Lombardo, Russel E. Caflisch, Marco Sammartino

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)69-82
Number of pages14
JournalJournal of Statistical Physics
Issue number1
StatePublished - Jan 2008


  • Boltzmann equation
  • Hydrodynamic limit
  • Navier-Stokes flow
  • Nonlocal boundary conditions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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