带加法白噪声的随机Boussinesq方程组的解的渐近行为

赵文强, 李扬荣

数学学报 ›› 2013, Vol. 56 ›› Issue (1) : 1-14.

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数学学报 ›› 2013, Vol. 56 ›› Issue (1) : 1-14. DOI: 10.12386/A2013sxxb0001
论文

带加法白噪声的随机Boussinesq方程组的解的渐近行为

    赵文强1, 李扬荣2
作者信息 +

Asymptotic Behavior of Stochastic Boussinesq Equations with Additive White Noises

    Wen Qiang ZHAO1, Yang Rong LI2
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文章历史 +

摘要

考虑速度和温度同时在加法白噪声扰动下的随机Boussinesq方程组的解的渐近特征.可以按轨道得到该随机方程组的唯一解,并可以验证该解生成随机动力系统,进而证明了该随机动力系统存在随机吸引子.

Abstract

This paper is devoted to the investigation of asymptotic behavior of stochastic Boussinesq equations influenced by random exterior forced white noises both in the velocity and in the temperature fields. It is showed that the stochastic Boussinesq equations can be solved path-wise and the unique solution generates a random dynamical system. Then the existence of a random attractor for the generated random dynamical system is established.

关键词

随机动力系统 / 随机Boussinesq方程组 / 随机吸引子 / 加法白噪声

Key words

random dynamical system / stochastic Boussinesq equations / random attractors / additive white noises

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赵文强, 李扬荣. 带加法白噪声的随机Boussinesq方程组的解的渐近行为. 数学学报, 2013, 56(1): 1-14 https://doi.org/10.12386/A2013sxxb0001
Wen Qiang ZHAO, Yang Rong LI. Asymptotic Behavior of Stochastic Boussinesq Equations with Additive White Noises. Acta Mathematica Sinica, Chinese Series, 2013, 56(1): 1-14 https://doi.org/10.12386/A2013sxxb0001

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基金

国家自然科学基金资助项目(11071199);重庆市教委科技资助项目(KJ120703);重庆市科委自然科学基金项目(cstc2012jjA00032);重庆工商大学博士启动基金项目(2012-56-09)

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