Rohde, ChristianTang, Hao2023-06-012023-06-0120201021-97221420-90041849829799http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-131236http://elib.uni-stuttgart.de/handle/11682/13123http://dx.doi.org/10.18419/opus-13104We consider a class of stochastic evolution equations that include in particular the stochastic Camassa-Holm equation. For the initial value problem on a torus, we first establish the local existence and uniqueness of pathwise solutions in the Sobolev spaces Hs with s>3/2. Then we show that strong enough nonlinear noise can prevent blow-up almost surely. To analyze the effects of weaker noise, we consider a linearly multiplicative noise with non-autonomous pre-factor. Then, we formulate precise conditions on the initial data that lead to global existence of strong solutions or to blow-up. The blow-up occurs as wave breaking. For blow-up with positive probability, we derive lower bounds for these probabilities. Finally, the blow-up rate of these solutions is precisely analyzed.eninfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/4.0/510article2023-03-28