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arXiv · 2301.04034

Existence and Blow-up of solutions for Stochastic Modified Two-component Camassa-Holm System

Wujun Lv·Xing Huang
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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 $H^{s}\times H^{s}, s>\frac{3}{2}$. 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.

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Wujun Lv, Xing Huang. 2023-01-10. Existence and Blow-up of solutions for Stochastic Modified Two-component Camassa-Holm System. https://arxiv.org/abs/2301.04034

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