随机旋转双分量Camassa-Holm系统的适定性和破波

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2023-08-01 DOI:10.1214/22-aap1877

Yong Chen, Jinqiao Duan, Hongjun Gao

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引用次数: 0

摘要

研究了随机旋转双分量Camassa-Holm（R2CH）系统的全局适定性和破波现象。首先，我们确定了R2CH系统的哈密顿结构，并使用随机哈密顿量导出随机R2CH系统。然后，利用离散耗散近似系统和正则化方法，建立了随机R2CH系统的局部适定性。我们还给出了随机R2CH系统的精确爆破准则。此外，我们还证明了随机R2CH系统的全局存在性是高概率的。最后，我们考虑了运输噪声的情况，建立了局部适定性和另一个爆破准则。

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

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 using a dispersion-dissipation approximation system and the regularization method. We also show a precise blow-up criterion for the stochastic R2CH system. Moreover, we prove that the global existence of the stochastic R2CH system occurs with high probability. At the end, we consider the transport noise case and establish the local well-posedness and another blow-up criterion.

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来源期刊

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.