Random Dynamics of the Boussinesq System with Dynamical Boundary Conditions
Random Dynamics of the Boussinesq System with Dynamical Boundary Conditions
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DOI：
10.1080/07362990902976546
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发表时间：
2009-08
影响因子：
1.3
通讯作者：
Peter Brune;Jinqiao Duan;B. Schmalfuß
中科院分区：
文献类型：
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作者：
Peter Brune;Jinqiao Duan;B. Schmalfuß
摘要 研究了二维纳维-斯托克斯方程和盐度输运方程的耦合系统，以及边界和流体中的空间相关白噪声。噪声通过动态边界条件影响系统。该系统可被视为海洋流体中重力流的模型。噪声是由于流体边界上盐度通量的不确定性造成的。将该系统转化为随机动力系统后，我们首先获得系统演化的渐近估计，然后表明长期动态是由随机吸引子捕获的。
Abstract A coupled system of the two-dimensional Navier–Stokes equations and the salinity transport equation with spatially correlated white noise on the boundary as well as in fluid is investigated. The noise affects the system through a dynamical boundary condition. This system may be considered as a model for gravity currents in oceanic fluids. The noise is due to uncertainty in salinity flux on fluid boundary. After transforming this system into a random dynamical system, we first obtain asymptotic estimates on system evolution, and then show that the long time dynamics is captured by a random attractor.