This paper is devoted to study the controllability of a one-dimensional fluid-particle interaction model where the fluid follows the viscous Burgers equation and the point mass obeys Newton’s second law. We prove the null controllability for the velocity of the fluid and the particle and an approximate controllability for the position of the particle with a control variable acting only on the particle. One of the novelties of our work is the fact that we achieve this controllability result in a uniform time for all initial data and without any smallness assumptions on the initial data.

中文翻译：

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关于带有粒子控制的粘性Burgers-粒子系统的全局零可控性

本文致力于研究一维流体-颗粒相互作用模型的可控性，其中流体遵循粘性Burgers方程，点质量服从牛顿第二定律。我们证明了流体和粒子速度的零可控性以及仅在粒子上具有控制变量的粒子位置的近似可控性。我们工作的新颖性之一是，对于所有初始数据，我们在统一的时间内获得了这种可控制性，并且对初始数据没有任何小小的假设。