Erratum to: Ghost effect by curvature in planar Couette flow [1]
Leif Arkeryd Raffaele Esposito Rossana Marra Anne Nouri
keywords: Couette flow. Boltzmann equation hydrodynamical limit ghost effect
A kinetic equation for spin polarized Fermi systems
Leif Arkeryd
This paper considers a kinetic Boltzmann equation, having a general type of collision kernel and modelling spin-dependent Fermi gases at low temperatures. The distribution functions have values in the space of positive hermitean $2\times2$ complex matrices. Global existence of weak solutions is proved in $L^1\cap L^{\infty}$ for the initial value problem of this Boltzmann equation in a periodic box.
keywords: low temperature kinetics. Fermi system with spin Boltzmann spin kinetics
A Milne problem from a Bose condensate with excitations
Leif Arkeryd Anne Nouri
This paper deals with a half-space linearized problem for the distribution function of the excitations in a Bose gas close to equilibrium. Existence and uniqueness of the solution, as well as its asymptotic properties are proven for a given energy flow. The problem differs from the ones for the classical Boltzmann and related equations, where the hydrodynamic mass flow along the half-line is constant. Here it is no more constant. Instead we use the energy flow which is constant, but no more hydrodynamic.
keywords: Milne problem. Low temperature kinetics Bose condensate two component model
Exponential stability of the solutions to the Boltzmann equation for the Benard problem
Leif Arkeryd Raffaele Esposito Rossana Marra Anne Nouri
We complete the result in [2] 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.
keywords: Boltzmann equation hydrodynamical limit Benard problem.
Ghost effect by curvature in planar Couette flow
Leif Arkeryd Raffaele Esposito Rossana Marra Anne Nouri
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 [18]). 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.
keywords: Couette flow. Boltzmann equation Ghost effect Hydrodynamical limit

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