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.