**Title: **Dissipation and mixing: from turbulent flows to weak solutions

**Abstract:** There is a well-known discrepancy in mathematical fluid mechanics between phenomena that we can observe and phenomena on which we have theorems. The challenge for the mathematician is then to formulate an existence theory of solutions to the equations of hydrodynamics which is able to reflect observation. The most important such observation, forming the backbone of turbulence theory, is anomalous dissipation. In the talk, we survey some of the recent developments concerning weak solutions in this context.

**About the speaker: **László Székelyhidi is Director at the Max Planck Institute for Mathematics in the Sciences in Leipzig and Professor of Fluid Mechanics at Leipzig University. He received his PhD in 2004 in Leipzig. His work focuses on the calculus of variations and mathematical fluid mechanics. In joint work with Camillo De Lellis, he developed a version of convex integration for the incompressible Euler equations for the construction of Hölder continuous weak solutions, a method that subsequently led to the resolution of Onsager’s celebrated conjecture and has been used since by many authors for the construction of weak solutions to various equations in mathematical fluid dynamics. In the academic year 2021/22 he was a Distinguished Visiting Professor at the Institute for Advanced Study in Princeton, where he organized the special year together with De Lellis. He is a member of the German National Academy of Sciences Leopoldina and the Hungarian Academy of Sciences and is a recipient of the Gottfried Wilhelm Leibniz Prize of the German Science Foundation.

This lecture is part of the program "Deterministic and Stochastic Analysis of Euler and Navier-Stokes Equations"