Stationary solutions to stochastic 3D Euler equations in Hölder space

Lin Lü; Rongchan Zhu

doi:10.1016/j.spa.2024.104465

Stationary solutions to stochastic 3D Euler equations in Hölder space

Lin Lü, Rongchan Zhu^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Article number	104465
Journal	Stochastic Processes and their Applications
Volume	177
DOIs	https://doi.org/10.1016/j.spa.2024.104465
Publication status	Published - Nov 2024

Keywords

Convex integration
Hölder space
Stationary solutions
Stochastic Euler equations

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10.1016/j.spa.2024.104465

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abstract = "We establish the existence of infinitely many global and stationary solutions in C(R,Cϑ) 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 Hofmanov{\'a} et al. (2022) and pathwise estimates to derive uniform moment estimates independent of time.",

keywords = "Convex integration, H{\"o}lder space, Stationary solutions, Stochastic Euler equations",

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AU - Lü, Lin

AU - Zhu, Rongchan

PY - 2024/11

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N2 - We establish the existence of infinitely many global and stationary solutions in C(R,Cϑ) 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.

AB - We establish the existence of infinitely many global and stationary solutions in C(R,Cϑ) 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.

KW - Convex integration

KW - Hölder space

KW - Stationary solutions

KW - Stochastic Euler equations

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DO - 10.1016/j.spa.2024.104465

M3 - Article

AN - SCOPUS:85201701068

SN - 0304-4149

VL - 177

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

M1 - 104465

ER -

Stationary solutions to stochastic 3D Euler equations in Hölder space

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Keywords

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