Equilibrating Effects of Boundary and Collision in Rarefied Gases

Hung-Wen Kuo, Tai Ping Liu, Li Cheng Tsai

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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
Volume328
Issue number2
DOIs
Publication statusPublished - 2014 Jan 1

Fingerprint

Rarefied Gas
rarefied gases
Boltzmann Equation
Collision
Knudsen number
Optimal Rate of Convergence
collisions
Exponential Convergence
Steady-state Solution
free molecular flow
Small Perturbations
Knudsen flow
Asymptotic Behavior
Boundary conditions
boundary conditions
perturbation
temperature

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Kuo, Hung-Wen ; Liu, Tai Ping ; Tsai, Li Cheng. / Equilibrating Effects of Boundary and Collision in Rarefied Gases. In: Communications in Mathematical Physics. 2014 ; Vol. 328, No. 2. pp. 421-480.
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Equilibrating Effects of Boundary and Collision in Rarefied Gases. / Kuo, Hung-Wen; Liu, Tai Ping; Tsai, Li Cheng.

In: Communications in Mathematical Physics, Vol. 328, No. 2, 01.01.2014, p. 421-480.

Research output: Contribution to journalArticle

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