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Loeb solutions of the Boltzmann equation. (English) Zbl 0598.76091

Existence problems for the Boltzmann equation constitute a main area of research within the kinetic theory of gases and transport theory. The present paper considers the spatially periodic case with \(L^ 1\) initial data. The main result is that the Loeb subsolutions [obtained by the author, ibid. 77, 1-10 (1981; Zbl 0547.76084)] are shown to be true solutions. The proof relies on the observation that monotone entropy and finite energy imply Loeb integrability of non-standard approximate solutions, and uses estimates from the proof of the H-theorem. Two aspects of the continuity of the solutions are also considered.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
45K05 Integro-partial differential equations

Citations:

Zbl 0547.76084
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References:

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