摘要：For the scalar advection-diffusion equation, according to physical predictions, the advecting velocity field, if turbulent, may enhance diffusion so strongly that a nontrivial dissipation of energy remains in the inviscid limit. This phenomenon – the strict energy inequality in the transport equation obtained as an inviscid limit – is referred to as ‘anomalous dissipation’. I will present a recent joint result with Burczak and Székelyhidi, proving that anomalous dissipation really occurs for scalars advected by a (typical) solution of Euler equation (with its regularity below the 1/3-Hölder continuity, the Onsager threshold). Consequently, we obtain non-uniqueness of the respective transport equations.
