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Exact and chapman‐enskog solutions for the carleman model
Author(s) -
Palczewski A.,
Neunzert H.
Publication year - 1984
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.1670060125
Subject(s) - mathematics , extension (predicate logic) , interval (graph theory) , exact solutions in general relativity , boltzmann equation , order (exchange) , mathematical analysis , thermodynamics , physics , combinatorics , finance , computer science , economics , programming language
The Chapman‐Enskog procedure is applied to the Carleman model of the Boltzmann equation. It has been proved that the Carleman equations possess a solution on the time interval on which a smooth solution of the fluid‐like equation exists. The calculations have been performed up to the first order i.e., to the Navier‐Stokes‐like equation. It has been shown that in this case a difference between an exact solution and the Chapman‐Enskog solution is of order ϵ 2 . Extension of the results to higher orders is also possible. This gives a justification of the Chapman‐Enskog procedure as an asymptotic expansion method.