数学
吸引子
不变(物理)
噪音的颜色
白噪声
数学分析
非线性系统
限制
有色的
动力系统理论
数学物理
物理
统计
机械工程
材料科学
量子力学
复合材料
工程类
作者
Tomás Caraballo,Zhang Chen,Dandan Yang
摘要
Abstract This paper is mainly concerned with the long‐term random dynamics for the nonautonomous 3D globally modified Navier–Stokes equations with nonlinear colored noise. We first prove the existence of random attractors of the nonautonomous random dynamical system generated by the solution operators of such equations. Then we establish the existence of invariant measures supported on the random attractors of the underlying system. Random Liouville‐type theorem is also derived for such invariant measures. Moreover, we further investigate the limiting relationship of invariant measures between the above equations and the corresponding limiting equations when the noise intensity approaches to zero. In addition, we show the invariant measures of such equations with additive white noise can be approximated by those of the corresponding equations with additive colored noise as the correlation time of the colored noise goes to zero.
科研通智能强力驱动
Strongly Powered by AbleSci AI