Equilibrating Effects of Boundary and Collision in Rarefied Gases

Hung Wen Kuo, Tai Ping Liu, Li Cheng Tsai

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


We investigate the time-asymptotic behavior for rarefied gases in the spherical domain with variable boundary temperature in ℝd, d = 1, 2, 3, under the diffuse reflection boundary condition. First, we obtain an optimal convergence rate of (1 + t)-d to the steady state for free molecular flow. Next, we use this to construct the steady state solution of the Boltzmann equation for sufficiently large Knudsen number and small boundary temperature variation. We also obtain an exponential convergence to the steady state for the Boltzmann equation for small perturbation.

Original languageEnglish
Pages (from-to)421-480
Number of pages60
JournalCommunications in Mathematical Physics
Issue number2
Publication statusPublished - 2014 Jun

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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