\(\alpha \) -稳定l过程驱动的随机Navier-Stokes方程的\(\alpha \) -依赖性不变测度

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-04-30 DOI:10.1007/s00245-025-10259-1

Ting Li, Xianming Liu

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引用次数: 0

摘要

本文主要研究了受\(\alpha \) -稳定圆柱噪声胁迫的Navier-Stokes方程的不变测度的收敛行为，这些噪声可以是非简并的，也可以是简并的。尽管不变测度缺乏唯一性，但我们成功地证明了在Wasserstein度量下，非简并噪声和简并噪声情况下不变测度收敛到对应的由布朗运动驱动的Navier-Stokes方程（\(\alpha \)趋于2）。特别地，对于非简并情形，在Wasserstein-1度规意义上建立了不变测度的收敛性。

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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The \(\alpha \)-Dependence of the Invariant Measure for the Stochastic Navier–Stokes Equation Driven by \(\alpha \)-Stable Lévy Processes

Our study focuses on the convergence behavior of invariant measures associated with Navier–Stokes equations forced by cylindrical \(\alpha \)-stable noises, which could be either non-degenerate or degenerate. Despite the absence of uniqueness in the invariant measures, we successfully demonstrate the convergence of invariant measures from both non-degenerate and degenerate noise cases to their corresponding Navier–Stokes equations driven by Brownian motions as \(\alpha \) tends to 2, under the Wasserstein metric. Especially, for the non-degenerate case, the convergence of invariant measures is established in the sense of the Wasserstein-1 metric.

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.