Well-posedness of the Cauchy problem for a space-dependent anyon Boltzmann equation

A fully non-linear kinetic Boltzmann equation for anyons and large initial data is studied in a periodic 1d setting. Strong L1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, and stability.Comment: 22 pages. In this version an earlier error has been corrected, and with it a study of the time asymptotics moved to a future paper. arXiv admin note: text overlap with arXiv:1207.059

On low temperature kinetic theory; spin diffusion, Bose Einstein condensates, anyons

The paper considers some typical problems for kinetic models evolving through pair-collisions at temperatures not far from absolute zero, which illustrate specific quantum behaviours. Based on these examples, a number of differences between quantum and classical Boltzmann theory is then discussed in more general terms.Comment: 25 pages, minor updates of previous versio

On a Boltzmann equation for Haldane statistics

The study of quantum quasi-particles at low temperatures including their statistics, is a frontier area in modern physics. In a seminal paper F.D. Haldane proposed a definition based on a generalization of the Pauli exclusion principle for fractional quantum statistics. The present paper is a study of quantum quasi-particles obeying Haldane statistics in a fully non-linear kinetic Boltzmann equation model with large initial data on a torus. Strong L1 solutions are obtained for the Cauchy problem. The main results concern existence, uniqueness and stability. Depending on the space dimension and the collision kernel, the results obtained are local or global in time.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1406.0265 This is the published version of the paper. The condition (2.3) on the collision kernel is strengthened, as required for the result to hol

On the Cauchy problem with large data for the space-dependent Boltzmann Nordheim equation III

This paper studies the quantum Boltzmann Nordheim equation from a Boltzmann equation for Haldane statistics. Strong solutions are obtained for the Cauchy problem with initial data in L1 and uniformly bounded on a one (resp. two or three)-dimensional torus for three-dimensional velocities and pseudo-Maxwellian (resp. very soft) forces. The main results are existence, uniqueness and stability of solutions conserving mass, momentum, and energy, with the uniform bound exploding if the solutions are only local in time.Comment: 20 pages. arXiv admin note: text overlap with arXiv:1711.10357, arXiv:1601.06927, arXiv:1611.0747

MR3434006 Arkeryd, Leif [Arkeryd, Leif O.] (S-CHAL); Nouri, Anne (F-AMU-IM) Well-posedness of the Cauchy problem for a space-dependent anyon Boltzmann equation. (English summary) SIAM J. Math. Anal. 47 (2015), no. 6, 4720{4742.

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