Stationary solutions to stochastic 3D Euler equations in H\"older space

Abstract

We establish the existence of infinitely many global and stationary solutions in $C(\mathbb{R};C^{\vartheta})$ space for some $\vartheta>0$ 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 \cite{HZZ22b} and pathwise estimates to derive uniform moment estimates independent of time.