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arXiv 1207.3255math.AP
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Navier-斯托克斯方程的不敏感控制

Insensitizing controls for the Navier-Stokes equations

Mamadou Gueye

摘要:

本文研究了具有Dirichlet边界条件的有界区域上Navier-斯托克斯方程的不敏感控制的存在性。我们证明,存在控制不敏感的$L^2$ -规范的观察的解决方案在一个开放的子集$\mathcal{O}$的域,在适当的假设下的数据。这个问题等价于级联系统的精确能控性结果。首先证明了具有右端的线性化Navier-Stokes系统的一个整体Carleman不等式,该不等式导致了系统在任意时刻的零能控性$T>0$ .然后,我们推导出一个局部零能控性结果的级联系统。

英文摘要:

In this paper, we deal with the existence of insensitizing controls for the Navier-Stokes equations in a bounded domain with Dirichlet boundary conditions. We prove that there exist controls insensitizing the $L^2$ -norm of the observation of the solution in an open subset $\mathcal{O}$ of the domain, under suitable assumptions on the data. This problem is equivalent to an exact controllability result for a cascade system. First we prove a global Carleman inequality for the linearized Navier-Stokes system with right-hand side, which leads to the null controllability at any time $T>0$. Then, we deduce a local null controllability result for the cascade system.

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