On the motion of a convex body interacting with a perfect gas in the mean-field approximation
We consider a convex body in R^3, moving along the x-axis, immersed in an infinitely extended perfect gas in the mean-field approximation. We assume that the gas particles interact with the body by means of elastic collisions. Giving to the body an initial velocity V_0, we prove that, for |V_0| sm...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
2007-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2007(2)/123-145.pdf |
| Summary: | We consider a convex body in R^3, moving along the x-axis, immersed in an infinitely extended perfect gas in the mean-field approximation. We assume that
the gas particles interact with the body by means of elastic collisions. Giving to the body an initial velocity V_0, we prove that, for |V_0| small enough, |V (t)| ≈ C t^{−5} for large t, being C a positive constant depending on the medium and on the shape of the obstacle. The power law approach to the equilibrium V = 0, instead of the exponential one (typical in viscous friction problems), is due to the long memory effect of the recollisions. This paper completes the analysis made in previous papers (see [7] and [8]), in which for simplicity the body was assumed to be a disk. |
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| ISSN: | 1120-7183 2532-3350 |