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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)2173-2191
Number of pages19
JournalNonlinearity
Volume31
Issue number5
DOIs
Publication statusPublished - 2018 Apr 9

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Knudsen number
Knudsen flow
Boltzmann equation
Nonlinear Stability
Boltzmann Equation
boxes
Convergence Rate
Term

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

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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.",
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Nonlinear stability of the 1D Boltzmann equation in a periodic box. / Wu, Kung-Chien.

In: Nonlinearity, Vol. 31, No. 5, 09.04.2018, p. 2173-2191.

Research output: Contribution to journalArticle

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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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