Speaker
Description
Scalar anomalous dissipation is a phenomenon in fluid dynamics in which a quantity advected by a fluid (e.g. the density of pollutant particles advected by a water current) is dissipated even 'without the final assistance of viscosity'. This behaviour has strong links to turbulence: in particular to Kolmogorov's 'zeroth law', to Onsager's theory, and to Richardson's hypothesis of turbulent trajectories.
In this series of talks I will present the recent result, obtained jointly with L. Székelyhidi and B. Wu, which shows that any scalar advected by a typical weak solution of the deterministic, incompressible 3D Euler equation exhibits anomalous dissipation.
The result combines two important developments in mathematical fluid mechanics: the application of convex integration methods, spearheaded by results of DeLellis and Székelyhidi, and the iterative quantitative homogenisation framework proposed recently by Armstrong and Vicol. I will provide some details on these two cornerstones, explain the necessary extensions that allowed us to combine them successfully, as well as the hydrodynamic context of our result.
