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On the initial layer and the existence theorem for the nonlinear Boltzmann equation
Author(s) -
Lachowicz M.,
Neunzert H.
Publication year - 1987
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.1670090127
Subject(s) - mathematics , boltzmann equation , mathematical analysis , euler equations , nonlinear system , boltzmann constant , euler's formula , interval (graph theory) , lattice boltzmann methods , initial value problem , physics , mechanics , thermodynamics , combinatorics , quantum mechanics
The truncated Hilbert expansion including the initial layer terms is considered. This enables us to replace the singulary perturbed Boltzmann equation by a weakly nonlinear equation. In this way the existence of a strong solution of the Boltzmann equation is obtained for initial data close enough to a local Maxwellian. The solution exists in the physically significant time interval on which smooth solutions to the Euler equations exist.