Geodesic
On the existence of a stationary measure for the stochastic system of the Lorenz model describing a baroclinic atmosphere
Sbornik. Mathematics, Tome 204 (2013) no. 9, pp. 1307-1331 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper is concerned with a nonlinear system of partial differential equations with parameters. This system describes the two-layer quasi-solenoidal Lorenz model for a baroclinic atmosphere on a rotating two-dimensional sphere. The right-hand side of the system is perturbed by white noise. Sufficient conditions on the parameters and the right-hand side are obtained for the existence of a stationary measure. Bibliography: 25 titles.
Keywords: two-layer quasi-solenoidal Lorenz model for a baroclinic atmosphere, existence of a stationary measure.
Mots-clés : white noise perturbation 
@article{SM_2013_204_9_a3,
     author = {Yu. Yu. Klevtsova},
     title = {On the existence of a~stationary measure for the stochastic system of the {Lorenz} model describing a~baroclinic atmosphere},
     journal = {Sbornik. Mathematics},
     pages = {1307--1331},
     year = {2013},
     volume = {204},
     number = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_9_a3/}
}
TY  - JOUR
AU  - Yu. Yu. Klevtsova
TI  - On the existence of a stationary measure for the stochastic system of the Lorenz model describing a baroclinic atmosphere
JO  - Sbornik. Mathematics
PY  - 2013
SP  - 1307
EP  - 1331
VL  - 204
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/SM_2013_204_9_a3/
LA  - en
ID  - SM_2013_204_9_a3
ER  - 
%0 Journal Article
%A Yu. Yu. Klevtsova
%T On the existence of a stationary measure for the stochastic system of the Lorenz model describing a baroclinic atmosphere
%J Sbornik. Mathematics
%D 2013
%P 1307-1331
%V 204
%N 9
%U http://geodesic.mathdoc.fr/item/SM_2013_204_9_a3/
%G en
%F SM_2013_204_9_a3
Yu. Yu. Klevtsova. On the existence of a stationary measure for the stochastic system of the Lorenz model describing a baroclinic atmosphere. Sbornik. Mathematics, Tome 204 (2013) no. 9, pp. 1307-1331. http://geodesic.mathdoc.fr/item/SM_2013_204_9_a3/

[1] Yu. Yu. Klevtsova, “Well-posedness of the Cauchy problem for the stochastic system for the Lorenz model for a baroclinic atmosphere”, Sb. Math., 203:10 (2012), 1490–1517 | DOI | DOI | MR

[2] B. V. Paltsev, Sfericheskie funktsii, Uchebno-metodicheskoe posobie, MFTI, M., 2000

[3] V. P. Dymnikov, Ustoichivost i predskazuemost krupnomasshtabnykh atmosfernykh protsessov, IVM RAN, M., 2007

[4] M. S. Agranovich, “Elliptic singular integro-differential operators”, Russian Math. Surveys, 20:5 (1965), 1–121 | DOI | MR | Zbl

[5] K. Yosida, Functional analysis, Grundlehren Math. Wiss., 123, Springer-Verlag, Berlin–Göttingen–Heidelberg; Academic Press, New York, 1965 | MR | MR | Zbl | Zbl

[6] Yu. N. Skiba, Matematicheskie voprosy dinamiki vyazkoi barotropnoi zhidkosti na vraschayuscheisya sfere, OVM AN SSSR, M., 1989

[7] S. G. Mikhlin, Multidimensional singular integrals and integral equations, Pergamon Press, Oxford–London–New York, 1965 | MR | MR | Zbl | Zbl

[8] S. G. Mikhlin, The problem of the minimum of a quadratic functional, Holden-Day, San Francisco–London–Amsterdam, 1965 | MR | MR | Zbl

[9] S. G. Mikhlin, “Differentsirovanie ryadov po sfericheskim funktsiyam”, Dokl. AN SSSR, 126:2 (1959), 278–279 | MR | Zbl

[10] S. G. Mikhlin, Lineinye uravneniya v chastnykh proizvodnykh, Vysshaya shkola, M., 1977 | MR

[11] A. V. Bulinskii, A. N. Shiryaev, Teoriya sluchainykh protsessov, Fizmatlit, M., 2005

[12] A. N. Shiryaev, Probability, Grad. Texts in Math., 95, Springer-Verlag, New York, 1996 | MR | Zbl

[13] O. Knill, Probability theory and stochastic processes with applications, Overseas Press, New Delhi, 2009

[14] G. Da Prato, J. Zabczyk, Stochastic equations in infinite dimensions, Encyclopedia Math. Appl., 44, Cambridge Univ. Press, Cambridge, 1992 | MR | Zbl

[15] I. M. Gel'fand, N. Ya. Vilenkin, Generalized functions, v. 4, Applications of harmonic analysis, Academic Press, New York–London, 1964 | MR | MR | Zbl | Zbl

[16] K. Kuratowski, Topology, v. 1, Academic Press, New York–London, 1966 | MR | MR | Zbl | Zbl

[17] I. I. Gihman, A. V. Skorohod, The theory of stochastic processes, v. II, Springer-Verlag, New York–Heidelberg, 1975 | MR | MR | Zbl | Zbl

[18] S. Kuksin, A. Shirikyan, Mathematics of two-dimensional turbulence, Cambridge Tracts in Mathematics, 194, Cambridge Univ. Press, Cambridge, 2012 | Zbl

[19] N. Ikeda, Sh. Watanabe, Stochastic differential equations and diffusion processes, North-Holland Math. Library, 24, North-Holland, Amsterdam–Oxford–New York, 1981 | MR | Zbl | Zbl

[20] Yu. N. Skiba, “Spectral approximation in the numerical stability study of nondivergent viscous flows on a sphere”, Numer. Methods Partial Differential Equations, 14:2 (1998), 143–157 | 3.0.CO;2-O class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[21] V. N. Krupchatnikov, G. P. Kurbatkin, Modelirovanie krupnomasshtabnoi dinamiki atmosfery. Metody diagnoza obschei tsirkulyatsii, VTs, Sib. otd-nie AN SSSR, Novosibirsk, 1991

[22] V. P. Dymnikov, A. N. Filatov, Mathematics of climate modeling, Model. Simul. Sci. Eng. Technol., Birkhäuser, Boston, MA, 1997 | MR | Zbl | Zbl

[23] A. S. Gorelov, “Dimension of the attractor for a two-layer baroclinic model”, Dokl. Earth Sciences, 345A:9 (1996), 1–7 | MR