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On stationary kinetic systems of Boltzmann type and their fluid limits

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Arkeryd L.

Banach Center Publications

2004

tom 66

nr 1

13-27

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.

Ograniczanie wyników

1 Banach Center Publications

1 Arkeryd L.

1 2004

Wyniki wyszukiwania

On stationary kinetic systems of Boltzmann type and their fluid limits