arXiv subjects

Leif Arkeryd

Publications and source records attributed to Leif Arkeryd.

3 recordsLinked to original sources

arXiv2021

Discrete velocity Boltzmann equation in the plane: stationary solutions

The paper proves existence of mild solutions to normal discrete velocity Boltzmann equations sin the plane with no pair of colinear interacting velocities, and given ingoing boundary values. A key property is L1 compactness of the integrated collision frequency for a sequence of approximations. This is proved using the Kolmogorov-Riesz theorem, which here replaces the L1 compactness of velocity averages, not available when the velocities are discrete.

math.AP↗

arXiv2016

On the Cauchy problem with large data for a space-dependent Boltzmann-Nordheim boson equation II

This paper studies a space-inhomogeneous Boltzmann-Nordheim equation with pseudo-Maxwellian forces. Strong solutions are obtained for the Cauchy problem in a setting with large bounded L1 initial data. The main results are existence, uniqueness, stability and qualitative boundedness features for solutions conserving mass, momentum and energy.

math-ph↗

arXiv2012

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.

math-ph↗