论文标题
在洛伦兹模型的固定措施的固定措施的无关限制上
On the inviscid limit of stationary measures for the stochastic system of the Lorenz model for a baroclinic atmosphere
论文作者
论文摘要
本文与具有参数和随机外力的偏微分方程的非线性系统有关。该系统描述了在旋转的二维球体上的斜压气氛的两层准螺旋洛伦兹模型。考虑了该问题的凯奇问题解决方案定义的马尔可夫半群的固定措施。突出显示了系统的一个参数 - 运动粘度的系数。当任何动力学粘度系数的任何序列均为零时，该系统的任何静态度量序列的限制性点都存在于限制的非平底点，从而得出了随机右侧和其他参数的足够条件。众所周知，实践中这种系数非常小。为限制度量证明了许多积分属性。此外，对于一个类似的斜压气体系统，获得了这些结果。
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 parameters 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.
