Il lavoro è suddiviso in due parti. La prima presenta un risultato recente dell'autore riguardante l'esistenza della soluzione dell'equazione di Boltzmann per molecole maxwelliane, senza alcun taglio nel nucleo del termine d'urto, quando la soluzione dipende da una sola variabile spaziale. A differenza del ben noto teorema di Di Perna-Lions, si dimostra che vale anche la conservazione dell'energia. La seconda parte presenta problemi di dinamica dei gas rarefatti, retti dall'equazione di Boltzmann riguardanti la teoria delle micromacchine (MEMS) e nanomacchine (NEMS).
Referenze Bibliografiche
[1] M. BONY, Existence globale et diffusion en théorie cinétique discrète, In Advances in Kinetic Theory and Continuum Mechanics, R. Gatignol and Soubbarameyer, Eds., 81-90, Springer-Verlag, Berlin (1991)
[5]
C. CERCIGNANI,
Estimating the solutions of the Boltzmann equation, submitted to
Jour. Stat. Phys. (
2005). |
fulltext (doi) |
MR 2266453[6]
C. CERCIGNANI -
R. ILLNER,
Global weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions,
Arch. Rational Mech. Anal. 134 (
1996), 1-16. |
fulltext (doi) |
MR 1392307 |
Zbl 0937.45007[8]
R. DIPERNA -
P. L. LIONS,
On the Cauchy problem for Boltzmann equations: Global existence and weak stability,
Ann. of Math. 130 (
1989), 321-366. |
fulltext (doi) |
MR 1014927 |
Zbl 0698.45010[9]
E. IKENBERRY -
C. TRUESDELL,
On the pressures and the flux of energy in a gas according to Maxwell's kinetic theory, I,
Jour. Rat. Mech. Anal. 5 (
1956), 1-54. |
MR 75725 |
Zbl 0070.23504[10] J. C. MAXWELL, On the dynamical theory of gases, Phil. Trans. Roy Soc. (London) 157 (1866), 49-88.
[12]
O. REYNOLDS,
On the theory of lubrication and its application to Mr. Beauchamp Tower's experiments including an experimental determination of the viscosity of the olive oil,
Philos. Trans. R. Soc. London,
A177 (
1886), 157-234. |
Zbl 18.0946.04[13] J. FAN - C. SHEN, Statistical simulation of low-speed unidirectional flows in transitional regime, in Rarefied Gas Dynamics, edited by R. Brun, R. Campargue, R. Gatignol, J.C. Lengrand, Cepadues Editions, Vol. 2 (1999), 245-252.
[14]
C. SHEN -
J. FAN -
C. XIE C,
Statistical simulation of rarefied gas flows in micro-channels,
J. Comp. Physics 189 (
2003), 512-526. |
Zbl 1061.76515[16] S. FUKUI - R. KANEKO, Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation: first report-derivation of a generalized lubrication equation including thermal creep flow, Journal of Tribology, 110 (1988), 253-262.
[17] S. FUKUI - R. KANEKO, Analysis of ultra-thin gas film lubrication based on the linearized Boltzmann equation, JSME International Journal, 30 (1987), 1660-1666.
[18] C. CERCIGNANI - M. LAMPIS - S. LORENZANI, Flow of a Rarefied Gas between Parallel and Almost Parallel Plates, in Rarefied Gas Dynamics, 24th Int. Symp., M. Capitelli Ed., AIP Conf. Proc. 762, pp. 719-724, New York (2005).
[19]
C. CERCIGNANI -
A. DANERI,
Flow of a rarefied gas between two parallel plates,
Journal of Applied Physics,
34 (
1963), 3509-3513. |
MR 160603[20]
F. J. ALEXANDER -
A.L. GARCIA -
B. J. ALDER,
Direct simulation Monte Carlo for thin film bearings,
Phys. Fluids,
6 (
1994), 3854-3860. |
Zbl 0832.76064