H\"older continuous solutions to stochastic 3D Euler equations via stochastic convex integration

In this paper, we are concerned with the three dimensional Euler equations driven by an additive stochastic forcing. First, we construct global H\"older continuous (stationary) solutions in C (R;C^) space for some >0 via a different method from LZ24. Our approach is based on applying stochastic convex integration to the construction of Euler flows in DelSze13 to derive uniform moment estimates independent of time. Second, for any divergence-free H\"older continuous initial condition, we show the existence of infinitely many global-in-time probabilistically strong and analytically weak solutions in Lᵖ₋₎₂ ([0, ) ;C^') C₋₎₂ ([0, ) ;H^-1) for all p [1, ) and some '>0.