Well-posedness and wave-breaking for the stochastic rotation-two-component Camassa-Holm system
 

Professor Hongjun Gao, School of Mathematics, Southeast University, Nanjing
 

Abstract：We study the global well-posedness and wave-breaking phenomenon for the stochastic rotation-two-component Camassa-Holm (R2CH) system. First, we find a Hamiltonian structure of the R2CH system and use the stochastic Hamiltonian to derive the stochastic R2CH system. Then, we establish the local well-posedness of the stochastic R2CH system by the dispersion-dissipation approximation system and the regularization method. We also show a precise blow-up criterion for the stochastic R2CH system. Moreover, we prove the global existence of the stochastic R2CH system occurs with high probability. At last, we consider transport noise case and establish the local well-posedness and another blow-up criterion.

The talk will be held via Zoom. Please contact Prof. Linghai Zhang (liz5@lehigh.edu) for additional information, as well as for the Zoom link/password.