Abstract
We study the effect of noise on the stochastic modified Camassa–Holm equation. We first derive the stochastic modified Camassa–Holm equation by the stochastic variational principle. Then, we prove the well-posedness of the stochastic modified Camassa–Holm equation by the iterative process. Under the condition of the small noise intensity, we can also get the regularization of the solution from the parabolic term.
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