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

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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
Issue number5
Publication statusPublished - 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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