Ghost effect by curvature in planar Couette flow

We study a rarefied gas, described by the Boltzmann equation, between two coaxial rotating cylinders in the small Knudsen number regime. When the radius of the inner cylinder is suitably sent to infinity, the limiting evolution is expected to converge to a modified Couette flow which keeps memory of the vanishing curvature of the cylinders (ghost effect). In the 1-d stationary case we prove the existence of a positive isolated L_2-solution to the Boltzmann equation and its convergence. This is obtained by means of a truncated bulk-boundary layer expansion which requires the study of a new Milne problem, and an estimate of the remainder based on a generalized spectral inequality.Comment: Revised version of the paper in Kinetic and related models, vol. 4 (2011) 109-13

Exponential stability of the solutions of the Boltzmann equation for the Benard problem

International audienceWe complete the result in the former paper 'Stability for Rayleigh-benard convective solutions of the Boltzmann equation' by showing the exponential decay of the perturbation of the laminar solution below the critical Rayleigh number and of the convective solutions above the critical Rayleigh number, in the kinetic framework

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 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. three)-dimensional torus for three-dimensional velocities and pseudo-Maxwellian (resp. very soft) forces

The kinetic and dynamic behaviour of a simple gas model

The so called Lebowitz stick model of a gas is studied. We discuss the particle level, as well as the gas kinetic, and gas dynamic levels of the model, and consider how the three levels are connected. In particular attention is given to the validation of the kinetic level from a stochastic Liouville equation, and to the asymptotic behaviour of the kinetic level