# Well-posedness of the Cauchy problem for the stochastic system for the Lorenz model for a baroclinic atmosphere

## 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.

- Authors:

- Siberian Regional Hydrometeorological Research Institute, Novosibirsk (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22094053

- Resource Type:
- Journal Article

- Journal Name:
- Sbornik. Mathematics

- Additional Journal Information:
- Journal Volume: 203; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ATMOSPHERES; CAUCHY PROBLEM; LAYERS; MATHEMATICAL SOLUTIONS; NOISE; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; RANDOMNESS; STOCHASTIC PROCESSES; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Klevtsova, Yulia Yu.
```*Well-posedness of the Cauchy problem for the stochastic system for the Lorenz model for a baroclinic atmosphere*. United States: N. p., 2012.
Web. doi:10.1070/SM2012V203N10ABEH004272.

```
Klevtsova, Yulia Yu.
```*Well-posedness of the Cauchy problem for the stochastic system for the Lorenz model for a baroclinic atmosphere*. United States. doi:10.1070/SM2012V203N10ABEH004272.

```
Klevtsova, Yulia Yu. Wed .
"Well-posedness of the Cauchy problem for the stochastic system for the Lorenz model for a baroclinic atmosphere". United States. doi:10.1070/SM2012V203N10ABEH004272.
```

```
@article{osti_22094053,
```

title = {Well-posedness of the Cauchy problem for the stochastic system for the Lorenz model for a baroclinic atmosphere},

author = {Klevtsova, Yulia Yu},

abstractNote = {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.},

doi = {10.1070/SM2012V203N10ABEH004272},

journal = {Sbornik. Mathematics},

issn = {1064-5616},

number = 10,

volume = 203,

place = {United States},

year = {2012},

month = {10}

}