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In this paper, we consider the Camassa-Holm equation posed on the periodic domain T. We show that Camassa-Holm equation is globally approximately controllable by three dimensional external force in Hˢ(T) for s > 3/2 . The proof is based on Agrachev-Sarychev approach in geometric control theory.
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Chowdhury et al. (2024) studied this question.
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