A Determining Form for the 2D Rayleigh-Bénard Problem
A Determining Form for the 2D Rayleigh-Bénard Problem
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发表时间：
2019-06
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通讯作者：
Yu Cao;M. Jolly;E. Titi
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作者：
Yu Cao;M. Jolly;E. Titi
作者：Cao，Yu; Jolly，Michael S; Titi，Edriss S|摘要：在无滑移和无应力边界条件下，我们构造了具有固体水平边界的条带中的2D Rayleigh-Benard（RB）系统的确定形式。确定的形式是一个常微分方程在Banach空间的轨迹，其稳定状态包括RB系统的长时间动态。实际上，RB系统的全局吸引子上的解可以通过常微分方程对每个初始轨迹约简到的标量方程的零点来进一步确定。在这项工作中的扭曲是，轨迹只为速度场，这反过来又决定了相应的温度轨迹。
Author(s): Cao, Yu; Jolly, Michael S; Titi, Edriss S | Abstract: We construct a determining form for the 2D Rayleigh-B #x27;enard (RB) system in a strip with solid horizontal boundaries, in the cases of no-slip and stress-free boundary conditions. The determining form is an ODE in a Banach space of trajectories whose steady states comprise the long-time dynamics of the RB system. In fact, solutions on the global attractor of the RB system can be further identified through the zeros of a scalar equation to which the ODE reduces for each initial trajectory. The twist in this work is that the trajectories are for the velocity field only, which in turn determines the corresponding trajectories of the temperature.