@article{44bccf5b254246919e23c552a7e2df65,
title = "Nonlinear stability of the 1D Boltzmann equation in a periodic box",
abstract = "We study the nonlinear stability of the Boltzmann equation in the 1D periodic box with size 1/ϵ, where 0 <ϵ≪ 1 is the Knudsen number. The convergence rate is (1 + t)-1/2 ln(1+t) for small time region and exponential for large time region. Moreover, the exponential rate depends on the size of the domain (Knudsen number). This problem is highly nonlinear and hence we need more careful analysis to control the nonlinear term.",
author = "Wu, {Kung Chien}",
note = "Funding Information: The author would like to thank Professor Tai-Ping Liu and Professor Kazuo Aoki for their encouragement and fruitful discussions concerning this project. This work is supported by the Ministry of Science and Technology under the grant 104-2628-M-006-003-MY4 and National Center for Theoretical Sciences. Publisher Copyright: {\textcopyright} 2018 BIPM & IOP Publishing Ltd.",
year = "2018",
month = apr,
day = "9",
doi = "10.1088/1361-6544/aaaf46",
language = "English",
volume = "31",
pages = "2173--2191",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "IOP Publishing Ltd.",
number = "5",
}