Existence and Blow-up of solutions for Stochastic Modified Two-component Camassa-Holm System
Probability
2023-01-11 v1
Abstract
In this paper, we consider the modified two-component Camassa-Holm System with multiplicative noise. For these SPDEs, we first establish the local existence and pathwise uniqueness of the pathwise solutions in Sobolev spaces . Then we show that strong enough noise can actually prevent blow-up with probability 1. Finally, we analyse the effects of weak noise and present conditions on the initial data that lead to the global existence and the blow-up in finite time of the solutions, and their associated probabilities are also obtained.
Keywords
Cite
@article{arxiv.2301.04034,
title = {Existence and Blow-up of solutions for Stochastic Modified Two-component Camassa-Holm System},
author = {Wujun Lv and Xing Huang},
journal= {arXiv preprint arXiv:2301.04034},
year = {2023}
}
Comments
29 pages. arXiv admin note: text overlap with arXiv:2003.07206 by other authors