霍尔德空间中随机三维欧拉方程的固定解

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2024-08-22 DOI:10.1016/j.spa.2024.104465

Lin Lü, Rongchan Zhu

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引用次数: 0

摘要

我们证明了在某些ϑ>0条件下，由加性随机强迫驱动的三维欧拉方程在C(R,Cϑ)空间中存在无限多个全局和静止解。该结果基于一种新的随机版凸积分法，结合了霍夫曼诺娃等人（2022）开发的随机凸积分法和路径估计法，得出了与时间无关的均匀矩估计值。

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Stationary solutions to stochastic 3D Euler equations in Hölder space

We establish the existence of infinitely many global and stationary solutions in $C (R, C^{ϑ})$ space for some $ϑ > 0$ to the three-dimensional Euler equations driven by an additive stochastic forcing. The result is based on a new stochastic version of the convex integration method, incorporating the stochastic convex integration method developed in Hofmanová et al. (2022) and pathwise estimates to derive uniform moment estimates independent of time.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.