# On stationary kinetic systems of Boltzmann type and their fluid limits

Banach Center Publications (2004)

- Volume: 66, Issue: 1, page 13-27
- ISSN: 0137-6934

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topLeif 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 -

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