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

Kazuo Aoki; Guido Cavallaro; Carlo Marchioro; Mario Pulvirenti

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

- Volume: 42, Issue: 2, page 263-275
- ISSN: 0764-583X

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topAoki, Kazuo, et al. "On the motion of a body in thermal equilibrium immersed in a perfect gas." ESAIM: Mathematical Modelling and Numerical Analysis 42.2 (2008): 263-275. <http://eudml.org/doc/250378>.

@article{Aoki2008,

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
$$
|V(t)-V\_\infty|\approx \frac\{C\}\{t^\{d+1\}\},
$$
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.
},

author = {Aoki, Kazuo, Cavallaro, Guido, Marchioro, Carlo, Pulvirenti, Mario},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Kinetic theory of gases; Boltzmann equation; free molecular gas; friction problem; approach to equilibrium.; approach to equilibrium},

language = {eng},

month = {3},

number = {2},

pages = {263-275},

publisher = {EDP Sciences},

title = {On the motion of a body in thermal equilibrium immersed in a perfect gas},

url = {http://eudml.org/doc/250378},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Aoki, Kazuo

AU - Cavallaro, Guido

AU - Marchioro, Carlo

AU - Pulvirenti, Mario

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2008/3//

PB - EDP Sciences

VL - 42

IS - 2

SP - 263

EP - 275

AB -
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
$$
|V(t)-V_\infty|\approx \frac{C}{t^{d+1}},
$$
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.

LA - eng

KW - Kinetic theory of gases; Boltzmann equation; free molecular gas; friction problem; approach to equilibrium.; approach to equilibrium

UR - http://eudml.org/doc/250378

ER -

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