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On the stationary Boltzmann equation

Leif Arkeryd

Séminaire Équations aux dérivées partielles

For stationary kinetic equations, entropy dissipation can sometimes be used in existence proofs similarly to entropy in the time dependent situation. Recent results in this spirit obtained in collaboration with A. Nouri, are here presented for the nonlinear stationary Boltzmann equation in bounded domains of I R n with given indata and diffuse reflection on the boundary.

On stationary kinetic systems of Boltzmann type and their fluid limits

Leif Arkeryd — 2004

Banach Center Publications

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....

On a functional equation arising in the kinetic theory of gases

Leif ArkerydCarlo Cercignani — 1990

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The problem of finding the summational collision invariants for the Boltzmann equation leads to a functional equation related to the Cauchy equation. The solution of this equation is known under different assumptions on its unknown ψ . Most proofs assume that the equation is pointwise satisfied, while the result needed in kinetic theory concerns the solutions of the equation when the latter is satisfied almost everywhere. The only results of this kind appear to be due to the authors of the present...

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