On stationary kinetic systems of Boltzmann type and their fluid limits

• Autorzy: Leif Arkeryd
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 76P05: Rarefied gas flows, Boltzmann equation
• 35Q35: PDEs in connection with fluid mechanics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2004
• Tom: 66
• Numer: 1
• Strony: 13-27

Daty

wydano

2004

Twórcy

autor

Leif Arkeryd

• Department of Mathematics, Chalmers University, S-41296 Gothenburg, Sweden

Identyfikatory

DOI

10.4064/bc66-0-1