Hölder solutions, fractal singularities and turbulence for the incompressible Euler equations

The motion of fluids in a turbulent regime turns out to be extremely chaotic. This makes their precise mathematical description very difficult and technical. Relying on the relatively new groundbreakings techniques introduced in this context by De Lellis and Székelyhidi I will explain how to date we can answer several mathematical questions that had a tremendous impact on both the mathematical and physical community. The talk will touch anomalous energy dissipation, the role of Hölder continuous weak solutions and fractal singularities in fully developed turbulence.