The Benjamin-Ono equation with 2D control input: approximate controllability and its application
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914509942161408 |
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| author | Zhao, Jia-Cheng |
| author_facet | Zhao, Jia-Cheng |
| contents | We establish the approximate controllability in $L^2$ for the nonlinear Benjamin-Ono equation on torus via two-dimensional control input. Our proof is based on adaptations of geometric control approach introduced by Agrachev and Sarychev. As an application of this control result, we study long-time dynamics of a randomly forced equation. It is proved that the trajectories are unbounded in Sobolev norms almost surely, when the random force is nondegenerate and statistically periodic in time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24130 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Benjamin-Ono equation with 2D control input: approximate controllability and its application Zhao, Jia-Cheng Optimization and Control Analysis of PDEs 35Q53, 35R60, 93B05 We establish the approximate controllability in $L^2$ for the nonlinear Benjamin-Ono equation on torus via two-dimensional control input. Our proof is based on adaptations of geometric control approach introduced by Agrachev and Sarychev. As an application of this control result, we study long-time dynamics of a randomly forced equation. It is proved that the trajectories are unbounded in Sobolev norms almost surely, when the random force is nondegenerate and statistically periodic in time. |
| title | The Benjamin-Ono equation with 2D control input: approximate controllability and its application |
| topic | Optimization and Control Analysis of PDEs 35Q53, 35R60, 93B05 |
| url | https://arxiv.org/abs/2604.24130 |