论文标题
粘性BousSinesQ系统的小型全球精确可控性
Small-time global exact controllability to the trajectories for the viscous Boussinesq system
论文作者
论文摘要
在本文中，我们处理了BousSinesQ系统轨迹的全球确切可控性。我们考虑2D和3D平滑界域。流体的速度磁场必须满足摩洛林边界条件的纳维尔滑移条件，并对温度施加了罗宾边界条件。我们假设一个人可以在边界的任意小部分上作用于速度和温度。证明依赖于三个主要论点。首先，我们通过使用域扩展程序将问题转换为分布式可控性问题。然后，我们通过遵循Coron等人的策略证明了全球近似可控性。欧元。数学。 Soc。，22（2020），第1625-1673页，涉及Navier-Stokes方程。该部分依赖于Inviscid Boussinesq系统和渐近边界层扩展的可控性。最后，我们以局部可控性结果得出结论，我们借助线性化参数和适当的卡尔曼估计来建立。
In this paper, we deal with the global exact controllability to the trajectories of the Boussinesq system. We consider 2D and 3D smooth bounded domains. The velocity field of the fluid must satisfy a Navier slip-with-friction boundary condition and a Robin boundary condition is imposed to the temperature. We assume that one can act on the velocity and the temperature on an arbitrary small part of the boundary. The proof relies on three main arguments. First, we transform the problem into a distributed controllability problem by using a domain extension procedure. Then, we prove a global approximate controllability result by following the strategy of Coron et al [J. Eur. Math. Soc., 22 (2020), pp. 1625-1673], which deals with the Navier-Stokes equations. This part relies on the controllability of the inviscid Boussinesq system and asymptotic boundary layer expansions. Finally, we conclude with a local controllability result that we establish with the help of a linearization argument and appropriate Carleman estimates.
