漂移项加控制的随机 Stokes 系统的零能控

Null controllablity of a stochastic Stokes system with control on the drift

摘要:

本文研究受控的正向随机Stokes系统的零能控问题.我们考虑满足如下给定条件的受控随机 Stokes系统:扩散项的系数为对角矩阵,且其对角元素为相同的有界随机过程.我们研究将控制加在漂移项的情形.在本文中我们利用Lebeau-Robbiano型的谱不等式得到倒向随机Stokes系统的部分能观性结果,从而得到受控正向随机Stokes系统在有限维子空间上的零能控,并且建立了不加控制的随机Stokes系统的解的高频部分能量的衰减性估计,最终通过迭代的方法得到此系统的零能控结果.

Abstract:

In this paper,we consider a controlled forward stochastic Stokes system with a diagonal matrix as the coefficient of diffusion term,and the diagonal matrix elements are the same bounded stochastic process.For the situation that only one control applied to the drift term,we use the Lebeau-Robbiano type spectral inequality to establish a “partial” observability estimate result,by which we get the the corresponding finite dimensional null controllability and establish the required decay estimate.Finally we derive the null controllability of the forward stochastic Stokes system.