Stationary solutions to stochastic 3D Euler equations in Hölder space

Abstract

We establish the existence of infinitely many global and stationary solutions in $C(R,C^{\vartheta })$ space for some $\vartheta >0$ 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.