论文标题
与麦克斯韦定律线性化的可压缩Navier-Stokes系统的一些可控性结果
Some Controllability Results for Linearized Compressible Navier-Stokes System with Maxwell's Law
论文作者
论文摘要
在本文中，我们研究了一维压缩的Navier-Stokes方程的控制方面，其麦克斯韦定律围绕稳定的稳定状态（零速度）线性化。我们考虑具有差异元边界条件和内部控制的线性化系统。我们证明，使用密度和应力方程中的局部控件，甚至速度方程中的任何地方控制系统都无法随时控制系统。但是，我们表明，如果在域中无处不在的密度或应力方程中的控制作用在密度或应力方程中，则该系统在任何时候都是无效的。这是该系统获得的最佳零可控性结果。接下来，我们证明使用本地化控件在很大程度上可以控制该系统。因此，我们的结果使朝这个方向完全了解系统。
In this article, we study the control aspects of the one-dimensional compressible Navier-Stokes equations with Maxwell's law linearized around a constant steady state with zero velocity. We consider the linearized system with Dirichlet boundary conditions and with interior controls. We prove that the system is not null controllable at any time using localized controls in density and stress equations and even everywhere control in the velocity equation. However, we show that the system is null controllable at any time if the control acting in the density or stress equation is everywhere in the domain. This is the best possible null controllability result obtained for this system. Next, we show that the system is approximately controllable at large time using localized controls. Thus, our results give a complete understanding of the system in this direction.
