The first part reviews some recent ideas and L¹-existence results for non-linear stationary equations of Boltzmann type in a bounded domain in ℝⁿ and far from global Maxwellian equilibrium. That is an area not covered by the DiPerna and P. L. Lions methods for the time-dependent Boltzmann equation from the late 1980-ies. The final part discusses the more classical perturbative case close to global equilibrium and corresponding small mean free path limits of fully non-linear stationary problems. Here the focus is on a particular two-rolls model problem including leading order hydrodynamic limits, but in a perspective of more general situations and the resolution of a variety of asymptotic stationary questions. Remarks are made about stationary solutions as long-time limits of corresponding time-dependent ones, and a number of open problems are also reviewed.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-1,
author = {Leif Arkeryd},
title = {On stationary kinetic systems of Boltzmann type and their fluid limits},
journal = {Banach Center Publications},
volume = {65},
year = {2004},
pages = {13-27},
zbl = {1059.76064},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-1}
}
Leif Arkeryd. On stationary kinetic systems of Boltzmann type and their fluid limits. Banach Center Publications, Tome 65 (2004) pp. 13-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-1/