分布路径依赖非线性 SPDEs 与随机传输型方程的应用

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-01-31 DOI:10.1007/s11118-023-10113-5

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引用次数: 0

摘要

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。

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

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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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.