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 Mat. Sb., 2017, Volume 208, Number 7, Pages 19–67 (Mi msb8659)

On the rate of convergence as $t\to+\infty$ of the distributions of solutions to the stationary measure for the stochastic system of the Lorenz model describing a baroclinic atmosphere

Yu. Yu. Klevtsovaab

a Siberian Regional Hydrometeorological Research Institute, Novosibirsk
b Siberian State University of Telecommunications and Informatics, Novosibirsk

Abstract: The paper is concerned with a nonlinear system of partial differential equations with parameters which 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. A unique stationary measure for the Markov semigroup defined by the solutions of the Cauchy problem for this problem is considered. An estimate for the rate of convergence of the distributions of all solutions in a certain class of this system to the unique stationary measure as $t\to+\infty$ is proposed. A similar result is obtained for the equation of a barotropic atmosphere and the two-dimensional Navier-Stokes equation. A comparative analysis with some of the available related results is given for the latter.
Bibliography: 39 titles.

Keywords: two-layer quasi-solenoidal Lorenz model for a baroclinic atmosphere, white noise perturbation, rate of convergence of the distributions of solutions to the stationary measure, the two-dimensional Navier-Stokes equation.

 Funding Agency Grant Number Russian Foundation for Basic Research 14-01-31110-ìîë_à This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 14-01-31110-ìîë_à).

DOI: https://doi.org/10.4213/sm8659

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English version:
Sbornik: Mathematics, 2017, 208:7, 929–976

Bibliographic databases:

UDC: 517.956.8
MSC: Primary 35G55; Secondary 35Q86

Citation: Yu. Yu. Klevtsova, “On the rate of convergence as $t\to+\infty$ of the distributions of solutions to the stationary measure for the stochastic system of the Lorenz model describing a baroclinic atmosphere”, Mat. Sb., 208:7 (2017), 19–67; Sb. Math., 208:7 (2017), 929–976

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb8659
• https://doi.org/10.4213/sm8659
• http://mi.mathnet.ru/eng/msb/v208/i7/p19

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This publication is cited in the following articles:
1. V. N. Krupchatnikov, G. A. Platov, E. N. Golubeva, A. A. Fomenko, Yu. Yu. Klevtsova, V. N. Lykosov, “Some Results of Studies in the Area of Numerical Weather Prediction and Climate Theory in Siberia”, Russ. Meteorol. Hydrol., 43:11 (2018), 713–721
2. S. Kuksin, A. Shirikyan, “Rigorous results in space-periodic two-dimensional turbulence”, Phys. Fluids, 29:12 (2017), 125106
3. Y. Liu, Zh. Wei, Ch. Li, A. Liu, L. Li, “Attractor and bifurcation of forced Lorenz-84 system”, Int. J. Geom. Methods Mod. Phys., 16:1 (2019), 1950002, 20 pp.
4. M. V. Kurgansky, V. N. Krupchatnikov, “Dynamic meteorology research in Russia, 2015-2018”, Izv. Atmos. Ocean. Phys., 55:6 (2019), 505–536
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