Global existence for the stochastic rotation-two-component Camassa–Holm system with nonlinear noise

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We study the well-posedness for the stochastic rotation-two-component Camassa–Holm (R2CH) system with the nonlinear noise. We establish the local well-posedness of the stochastic R2CH system by the dispersion–dissipation approximation system and the regularization method. We also prove the global existence of the stochastic R2CH system with a large nonlinear noise.