Behind the mirror: The hidden dissipative singular solutions of ideal reversible fluids on log-lattices

We explore how efficiency, a measure of the energy stored in a flow, governs the transition from smooth, viscous dynamics to singular, inviscid ones. Using fluids on log-lattices within a reversible framework, we reveal self-similar blow-ups and their continuation beyond blow-up through stochastic friction. These post-blow-up states connect non-dissipative and dissipative regimes, offering a dynamical route to construct singular solutions of the Euler equations.