Keywords: Markov processes with a local interaction, scaling, hydrodynamics.
@article{TVP_2008_53_4_a9,
author = {V. A. Malyshev and A. D. Manita},
title = {Stochastic {Micromodel} of the {Couette} {Flow}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {798--809},
year = {2008},
volume = {53},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_4_a9/}
}
V. A. Malyshev; A. D. Manita. Stochastic Micromodel of the Couette Flow. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 4, pp. 798-809. http://geodesic.mathdoc.fr/item/TVP_2008_53_4_a9/
[1] Strannye attraktory, Matematika. Novoe v zarubezhnoi nauke, 22, Mir, M., 1981 | MR
[2] Chorin A. J., Marsden J. E., A Mathematical Introduction to Fluid Mechanics, Springer-Verlag, New York, 1993, 169 pp. | Zbl
[3] Marchioro C., Pulvirenti M., Mathematical Theory of Incompressible Non Viscous Fluids, Springer-Verlag, New York, 1994, 283 pp. | MR
[4] Shiryaev A., On the classical, statistical, and stochastic approaches to the hydrodynamic turbulence, Research Report No 2, Thiele Centre for Applied Mathematics in Natural Science, Aarhus, 2007
[5] Kolmogorov A. N., “Matematicheskie modeli turbulentnogo dvizheniya neszhimaemoi vyazkoi zhidkosti”, Uspekhi matem. nauk, 59:1 (2004), 5–10 | MR
[6] Meshalkin L. D., Sinai Ya. G., “Issledovanie ustoichivosti statsionarnogo resheniya odnoi sistemy uravnenii ploskogo dvizheniya neszhimaemoi vyazkoi zhidkosti”, Prikl. matem. i mekh., 25 (1965), 1140–1143
[7] Landau L. D., Akhiezer A. I., Lifshits E. M., Kurs obschei fiziki. Mekhanika i molekulyarnaya fizika, Nauka, M., 1966, 384 pp.
[8] Liggett T., Markovskie protsessy s lokalnym vzaimodeistviem, Mir, M., 1989, 550 pp. | MR | Zbl
[9] Kipnis C., Landim C., Scaling Limits of Interacting Particle Systems, Springer-Verlag, Berlin, 1999, 442 pp. | MR
[10] Spohn H., Large Scale Dynamics of Interacting Particles, Springer-Verlag, Berlin, 1991, 342 pp.
[11] Esposito R., Marra R., Yau H. T., “Navier–Stokes equations for stochastic particle systems on the lattice”, Comm. Math. Phys., 182:2 (1996), 395–456 | DOI | MR
[12] Ignatyuk I. A., Malyshev V. A., Molchanov S. A., “Moment-closed processes with local interaction”, Selecta Math. Soviet., 8:4 (1989), 351–384 | MR | Zbl
[13] Méléard S., “Monte-Carlo approximations for 2d Navier–Stokes equations with measure initial data”, Probab. Theory Related Fields, 121:3 (2001), 367–388 | DOI | MR | Zbl
[14] Fontbona J., “A probabilistic interpretation and stochastic particle approximations of the 3-dimensional Navier–Stokes equations”, Probab. Theory Related Fields, 136:1 (2006), 102–156 | DOI | MR | Zbl
[15] Golinelli O., Mallick K., “Derivation of a matrix product representation for the asymmetric exclusion process from algebraic Bethe ansatz”, J. Phys. A, 39:34 (2006), 10647–10658 | DOI | MR | Zbl
[16] Derrida B., Lebowitz J. L., Speer E. R., “Entropy of open lattice systems”, J. Statist. Phys., 126:4–5 (2006), 1083–1108 | MR