On the motion of a body in thermal equilibrium immersed in a perfect gas
Aoki, Kazuo ; Cavallaro, Guido ; Marchioro, Carlo ; Pulvirenti, Mario
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008), p. 263-275 / Harvested from Numdam
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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 ∞ and prove that, under suitable smallness assumptions, the approach to equilibrium is |V(t)-V ∞ |≈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.

Publié le : 2008-01-01
DOI : https://doi.org/10.1051/m2an:2008007
Classification:  76P05,  82B40,  82C40,  35L45,  35L50 
@article{M2AN_2008__42_2_263_0,
     author = {Aoki, Kazuo and Cavallaro, Guido and Marchioro, Carlo and Pulvirenti, Mario},
     title = {On the motion of a body in thermal equilibrium immersed in a perfect gas},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {42},
     year = {2008},
     pages = {263-275},
     doi = {10.1051/m2an:2008007},
     mrnumber = {2405148},
     zbl = {1133.76046},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2008__42_2_263_0}
}

Aoki, Kazuo; Cavallaro, Guido; Marchioro, Carlo; Pulvirenti, Mario. On the motion of a body in thermal equilibrium immersed in a perfect gas. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008) pp. 263-275. doi : 10.1051/m2an:2008007. http://gdmltest.u-ga.fr/item/M2AN_2008__42_2_263_0/

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