Stationary solutions to stochastic 3D Euler equations in Hölder space

2024/01/18 by Lin Lü, Lü, Lin, Rongchan Zhu +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Analysis of PDEs (math.AP) #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2401.09894

openalex publication_date 2024/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 noise. The result is based on a new stochastic version of the convex integration method, incorporating the stochastic convex integration method developed in \citeHZZ22b and pathwise estimates to derive uniform moment estimates independent of time.

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• Dissipative solutions to randomly forced 3D Euler equations

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