This article is cited in 4 scientific papers (total in 4 papers)
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
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.
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.
|Russian Foundation for Basic Research
|This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 14-01-31110-мол_а).
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Sbornik: Mathematics, 2017, 208:7, 929–976
MSC: Primary 35G55; Secondary 35Q86
Received: 12.01.2016 and 02.03.2017
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
\paper 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
\jour Mat. Sb.
\jour Sb. Math.
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