On the motion of a body in thermal equilibrium immersed in a perfect gas

• Aoki, Kazuo

• Cavallaro, Guido

• Marchioro, Carlo

• Pulvirenti, Mario

Abstract

We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity V(t) to the limiting velocity $V_infty$ and prove that, under suitable smallness assumptions, the approach to equilibrium is begin{displaymath}vert V(t)-V_inftyvertapprox frac{C}{t^{d+1}}, end{displaymath} where d is the dimension of the space, and C is a positive constant. This approach is not exponential, as typical in friction problems, and even slower than for the same problem with elastic collisions.

Journal

• ESAIM: Mathematical Modelling and Numerical Analysis

  ESAIM: Mathematical Modelling and Numerical Analysis 42 (2), 263-275, 2008-03

  EDP Sciences, SMAI

Keywords

• kinetic theory of gases
• Boltzmann equation
• freemolecular gas
• friction problem
• approach to equilibrium

Details

• CRID: 1050282677039797760
• NII Article ID: 120001462593
• NII Book ID: AA1196611X
• ISSN: 0764583X
• HANDLE: 2433/84651
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • CiNii Articles