Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2604.24130

Author: Zhao, Jia-Cheng

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Peking University

OpenAlex ID: W7156645082

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