Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-31 DOI:10.1007/s11118-023-10113-5

引用次数: 0

Abstract

By using a regularity approximation argument, the global existence and uniqueness are derived for a class of nonlinear SPDEs depending on both the whole history and the distribution under strong enough noise. As applications, the global existence and uniqueness are proved for distribution-path dependent stochastic transport type equations, which are arising from stochastic fluid mechanics with forces depending on the history and the environment. In particular, the distribution-path dependent stochastic Camassa-Holm equation with or without Coriolis effect has a unique global solution when the noise is strong enough, whereas for the deterministic model wave-breaking may occur. This indicates that the noise may prevent blow-up almost surely.

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分布路径依赖非线性 SPDEs 与随机传输型方程的应用

摘要通过使用正则近似论证，推导出一类非线性 SPDE 在足够强的噪声下的全局存在性和唯一性。作为应用，证明了分布路径依赖随机输运型方程的全局存在性和唯一性，这些方程产生于随机流体力学，其作用力取决于历史和环境。特别是，当噪声足够强时，有或没有科里奥利效应的分布路径依赖随机卡马萨-霍尔姆方程具有唯一的全局解，而对于确定性模型，则可能出现破波现象。这表明，噪声几乎肯定可以防止炸波。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.