Premium
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom