Geodesic
On the inviscid limit of stationary measures for the stochastic system of the Lorenz model for a baroclinic atmosphere
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 1015-1037

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is concerned with a nonlinear system of partial differential equations with parameters and the random external force. This system describes the two-layer quasi-solenoidal Lorenz model for a baroclinic atmosphere on a rotating two-dimensional sphere. The stationary measures for the Markov semigroup defined by the solutions of the Cauchy problem for this problem is considered. One parameter of the system is highlighted – the coefficient of kinematic viscosity. The sufficient conditions on the random right-hand side and the other param-ters are derived for the existence of a limiting nontrivial point for any sequence of the stationary measures for this system when any sequence of the kinematic viscosity coefficients goes to zero. As it is well known, this coefficient in practice is extremely small. A number of integral properties are proved for the limiting measure. In addition, these results are obtained for one similar baroclinic atmosphere system.
Keywords: baroclinic atmosphere, Lorenz model, random external force, stationary measure
Mots-clés : inviscid limit. 
@article{SEMR_2022_19_2_a42,
     author = {Yu. Yu. Klevtsova},
     title = {On the inviscid limit of stationary measures for the stochastic system of the {Lorenz} model for a baroclinic atmosphere},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1015--1037},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a42/}
}
TY  - JOUR
AU  - Yu. Yu. Klevtsova
TI  - On the inviscid limit of stationary measures for the stochastic system of the Lorenz model for a baroclinic atmosphere
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2022
SP  - 1015
EP  - 1037
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a42/
LA  - en
ID  - SEMR_2022_19_2_a42
ER  - 
%0 Journal Article
%A Yu. Yu. Klevtsova
%T On the inviscid limit of stationary measures for the stochastic system of the Lorenz model for a baroclinic atmosphere
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2022
%P 1015-1037
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a42/
%G en
%F SEMR_2022_19_2_a42
Yu. Yu. Klevtsova. On the inviscid limit of stationary measures for the stochastic system of the Lorenz model for a baroclinic atmosphere. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 1015-1037. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a42/