Nonlinear stability of the 1D Boltzmann equation in a periodic box

Kung Chien Wu

doi:10.1088/1361-6544/aaaf46

Nonlinear stability of the 1D Boltzmann equation in a periodic box

Kung Chien Wu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	2173-2191
Number of pages	19
Journal	Nonlinearity
Volume	31
Issue number	5
DOIs	https://doi.org/10.1088/1361-6544/aaaf46
Publication status	Published - 2018 Apr 9

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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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",

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T1 - Nonlinear stability of the 1D Boltzmann equation in a periodic box

AU - Wu, Kung Chien

N1 - 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: © 2018 BIPM & IOP Publishing Ltd.

PY - 2018/4/9

Y1 - 2018/4/9

N2 - 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.

AB - 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.

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EP - 2191

JO - Nonlinearity

JF - Nonlinearity

IS - 5

ER -

Nonlinear stability of the 1D Boltzmann equation in a periodic box

Abstract

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