Stationary solutions to stochastic 3D Euler equations in Hölder space (Q6615517)

The authors consider stochastic Euler equations on the three dimensional torus and driven by additive noise, with the purposes of showing the existence and nonuniqueness of global Hölder continuous solutions and stationary solutions. The proofs are based on the stochastic convex integration method developed in [\textit{M. Hofmanová} et al., ``Non-unique ergodicity for deterministic and stochastic 3D Navier-Stokes and Euler equations'', Preprint, \url{arXiv:2208.08290}], which overcomes the limitation of stopping times, and on pathwise estimates during iteration for convex integration and a cutoff technique for controlling pathwisely the growth of noise.