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arXiv · 2604.24130

The Benjamin-Ono equation with 2D control input: approximate controllability and its application

Jia-Cheng Zhao
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Abstract

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.

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Jia-Cheng Zhao. 2026-04-27. The Benjamin-Ono equation with 2D control input: approximate controllability and its application. https://arxiv.org/abs/2604.24130

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