Abstract:
The paper is concerned with the Cauchy problem for 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, and random initial data is considered. This system is shown to be uniquely solvable, and an estimate for the continuous dependence of the solution on the set of random initial data and the right-hand side is established on a finite time interval. In passing, an estimate for the continuous dependence on the set of parameters, the initial
data, and the right-hand side is obtained on a finite time interval for the solution of the Cauchy problem with
deterministic initial data and deterministic right-hand side.
Bibliography: 32 titles.
Keywords:
two-layer quasi-solenoidal Lorenz model for a baroclinic atmosphere, white noise perturbation, well-posed Cauchy problem, random initial data.
Citation:
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
\Bibitem{Kle12}
\by Yu.~Yu.~Klevtsova
\paper Well-posedness of the Cauchy problem for the stochastic system for the Lorenz model for a~baroclinic atmosphere
\jour Sb. Math.
\yr 2012
\vol 203
\issue 10
\pages 1490--1517
\mathnet{http://mi.mathnet.ru/eng/sm7887}
\crossref{https://doi.org/10.1070/SM2012v203n10ABEH004272}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3027139}
\zmath{https://zbmath.org/?q=an:06134395}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000312249700004}
\elib{https://elibrary.ru/item.asp?id=19066342}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84872283957}
Linking options:
https://www.mathnet.ru/eng/sm7887
https://doi.org/10.1070/SM2012v203n10ABEH004272
https://www.mathnet.ru/eng/sm/v203/i10/p117
This publication is cited in the following 6 articles:
Yu. Yu. Klevtsova, “On the inviscid limit of stationary measures for the stochastic system of the Lorenz model for a baroclinic atmosphere”, Sib. elektron. matem. izv., 19:2 (2022), 1015–1037
Krupchatnikov V.N., Platov G.A., Golubeva E.N., Fomenko A.A., Klevtsova Yu.Yu., Lykosov V.N., “Some Results of Studies in the Area of Numerical Weather Prediction and Climate Theory in Siberia”, Russ. Meteorol. Hydrol., 43:11 (2018), 713–721
Yu. Yu. Klevtsova, “On the rate of convergence as t→+∞ of the distributions of solutions to the stationary measure for the stochastic system of the Lorenz model describing a baroclinic atmosphere”, Sb. Math., 208:7 (2017), 929–976
Yu. Yu. Klevtsova, “The uniqueness of a stationary measure for the stochastic system of the Lorenz model describing a baroclinic atmosphere”, Sb. Math., 206:3 (2015), 421–469
Yu. Yu. Klevtsova, “On the existence of a stationary measure for the stochastic system of the Lorenz model describing a baroclinic atmosphere”, Sb. Math., 204:9 (2013), 1307–1331
Citation in format AMSBIB
Contact us: