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Analysis shows global approximate controllability and prevention of solutions' blow up in H^s with external force.
In this article, we consider the Camassa-Holm equation posed on the periodic domain T. We show that in any positive time, the Camassa-Holm equation is globally approximately controllable in Hˢ(T) for s > 3/2 by a three dimensional external force. The proof is based on Agrachev-Sarychev approach in geometric control theory. In particular, our three dimensional control prevents a finite time blow up of the solution of Camassa-Holm equation in Hˢ(T) for s > 3/2.
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Chowdhury et al. (2025) studied this question.
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