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Scaling limits for the Ruijgrok–Wu model of the Boltzmann equation
Author(s) -
Gabetta Ester,
Perthame Benoît
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.251
Subject(s) - burgers' equation , limit (mathematics) , mathematics , boltzmann equation , conservation law , scaling , mathematical physics , kinetic theory , scaling law , statistical physics , scaling limit , partial differential equation , mathematical analysis , physics , thermodynamics , geometry
The Ruijgrok–Wu model of the kinetic theory of rarefied gases is investigated both in the fluid‐dynamic and hydro‐dynamic scalings. It is shown that the first limit equation is a first order quasilinear conservation law, whereas the limit equation in the diffusive scaling is the viscous Burgers equation. The main difficulties came from initial layers that we handle here. Copyright © 2001 John Wiley & Sons, Ltd.