A stochastic convex integration scheme for the intermittent Onsager theorem in two-dimensional domains

For any $γ\in \left[ {0,\frac{1}{3}} \right)$, we construct $γ$-Hölder-continuous martingale solutions to the two-dimensional stochastic incompressible Euler equations. These martingale solutions exhibit dissipative behavior and intermittency, thereby establishing the flexible part of the intermitte