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.


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


Zbl 0547.76084
Full Text: DOI


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