发表机构
Université de Monastir, Faculté des Sciences de Monastir; New York University Abu Dhabi（莫纳斯提尔大学，莫纳斯提尔理学院; 纽约大学阿布扎比分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究有界多连通平面Lipschitz区域中点涡系统的边界可控性，分别证明时变控制下的精确轨迹可控性与定常控制下的精确端点可控性，还探讨了最优控制的存在性问题。
AI 中文摘要
本文研究有界多连通平面Lipschitz区域中有限点涡系统的边界可控性，控制施加于边界任意非空相对开子集的局部区域，假设边界流入部分无入射涡量。对于时变控制，证明了沿任意指定的、远离边界的无碰撞涡路径的精确轨迹可控性；对于定常控制，证明了与互不相交实解析弧相关的精确端点可控性。证明依赖于调和插值、局部Runge逼近和隐函数论证，还研究了使轨迹长度最小的最优控制，证明了在稍光滑控制类中不存在极小元，并在控制时间和控制大小受惩罚时建立了存在性。
英文摘要
In this article, we investigate the boundary controllability of finite point-vortex systems in bounded multiply connected planar Lipschitz domains. The controls are applied locally on an arbitrary nonempty relatively open subset of the boundary. Zero incoming vorticity is assumed at the inflow part of the boundary. For time-dependent controls, we prove exact trajectory controllability along arbitrary prescribed collision-free vortex paths remaining away from the boundary. For stationary controls, we prove exact endpoint controllability associated with mutually disjoint real-analytic arcs. The proofs rely on harmonic interpolation, localized Runge approximation, and an implicit-function argument. The optimal control minimizing the length of trajectories is also studied. We prove the nonexistence of minimizers within classes of slightly smooth controls, and establish existence when the control time and the size of the control are penalized.
