Loeb solutions of the Boltzmann equation (Q1080319)

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.