On the inviscid limit of stationary measures for the Lorentz model of a baroclinic atmosphere

One nonlinear system of partial differential equations with parameters perturbed by white noise is considered. This system describes a two-layer quasi-solenoidal Lorentz model of a baroclinic atmosphere on a rotating two-dimensional sphere. Stationary measures of a Markov semigroup defined by solutions of the Cauchy problem for this system are considered. One parameter of the system is allocated − the coefficient of kinematic viscosity. Sufficient conditions are derived for the remaining parameters and a random external force for the existence of a limiting nontrivial point of any sequence of stationary measures of this system, when any sequence of kinematic viscosity coefficients tends to zero. As is well known, the kinematic viscosity coefficient is extremely small in practice. It is shown that only with white noise, proportional to the square root of the kinematic viscosity coefficient, there is a non-trivial limit.