Pointwise Behavior of the Linearized Boltzmann Equation on Torus
Abstract
We study the pointwise behavior of the linearized Boltzmann equation on torus for non-smooth initial perturbation. The result reveals both the fluid and kinetic aspects of this model. The fluid-like waves are constructed as part of the long-wave expansion in the spectrum of the Fourier mode for the space variable, the time decay rate of the fluid-like waves depends on the size of the domain. We design a Picard-type iteration for constructing the increasingly regular kinetic-like waves, which are carried by the transport equations and have exponential time decay rate. Moreover, the mixture lemma plays an important role in constructing the kinetic-like waves, we supply a new proof of this lemma to avoid constructing explicit solution of the damped transport equations
Cite
@article{arxiv.1301.0734,
title = {Pointwise Behavior of the Linearized Boltzmann Equation on Torus},
author = {Kung-Chien Wu},
journal= {arXiv preprint arXiv:1301.0734},
year = {2013}
}