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PreprintarXiv licencearXiv

Boundary Control of Two-dimensional Point-Vortex Systems

  • Kaïs Ammari
  • Taoufik Hmidi
  • Haocheng Yang
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{ammari2026boundary,
  title = {{Boundary Control of Two-dimensional Point-Vortex Systems}},
  author = {Kaïs Ammari and Taoufik Hmidi and Haocheng Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11564},
  eprint = {2610.11564},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11564},
}
RIS
TY  - UNPB
TI  - Boundary Control of Two-dimensional Point-Vortex Systems
AU  - Kaïs Ammari
AU  - Taoufik Hmidi
AU  - Haocheng Yang
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11564
UR  - https://arxiv.org/abs/2610.11564
AB  - 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.
ER  -