On stationary kinetic systems of Boltzmann type and their fluid limits

Leif Arkeryd. "On stationary kinetic systems of Boltzmann type and their fluid limits." Banach Center Publications 66.1 (2004): 13-27. <http://eudml.org/doc/282533>.

@article{LeifArkeryd2004,
abstract = {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.},
author = {Leif Arkeryd},
journal = {Banach Center Publications},
keywords = {kinetic systems; fluid limits; -existence; perturbation},
language = {eng},
number = {1},
pages = {13-27},
title = {On stationary kinetic systems of Boltzmann type and their fluid limits},
url = {http://eudml.org/doc/282533},
volume = {66},
year = {2004},
}

TY - JOUR
AU - Leif Arkeryd
TI - On stationary kinetic systems of Boltzmann type and their fluid limits
JO - Banach Center Publications
PY - 2004
VL - 66
IS - 1
SP - 13
EP - 27
AB - 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.
LA - eng
KW - kinetic systems; fluid limits; -existence; perturbation
UR - http://eudml.org/doc/282533
ER -