Some Recent Results on Stochastic Camass-Holm Type Equations: Global Existence, Blow-Up and Stability
Yingting Miao
Xi'an Jiaotong-Liverpool University Peoples Rep of China
Co-Author(s):
Abstract:
This presentation discusses results on stochastic Camass-Holm type equations. We examine the impact of noise on global existence, blow-up and stability. We identify a family of nonlinear noises that prevent blow-up with probability 1. In the case of linear noise, we demonstrate that singularities occur in finite time with positive probability and provide lower bounds for these probabilities. Finally, we introduce the concept of stability of the exiting time, showing that one cannot improve the stability of the exiting time and simultaneously improve the continuity of the dependence on initial data.