色噪声驱动三维CBF方程的随机指数吸引子

Random Exponential Attractor for 3D CBF Equations Driven by Colored Noise

摘要

利用解的先验估计、Lipschitz连续性及解的高频挤压估计,研究由色噪声驱动的随机对流Brinkman-Forchheimer(CBF)方程解的稳定性与分形维数有限性问题,得到了该方程随机指数吸引子的存在性.

Abstract

By using the prior estimates, Lipschitz continuity and squeezing estimates of the high frequency of the solutions, we studied the problems of stability and finiteness of fractal dimension of solutions to the stochastic convection Brinkman-Forchheimer (CBF) equations driven by colored noise, and obtained the existence of random exponential attractors for these equations.

关键词

色噪声 / 分形维数 / 对流Brinkman-Forchheimer方程 / 随机指数吸引子

Key words

colored noise / fractal dimension / convection Brinkman-Forchheimer equation / random exponential attractor

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基金资助

国家自然科学基金(12271141)