Anomalous Dissipation and the Strong Onsager Conjecture - Part 1: The Local Energy Inequality

Explore the intricacies of anomalous dissipation and the Strong Onsager Conjecture in this 58-minute lecture from Max Planck Science. Delve into the phenomenon of unusual energy losses in physical systems, particularly turbulent flows, and understand how energy from macroscopic motions is transferred to smaller scales and dissipated as heat. Examine Lars Onsager's hypothesis on the mathematical description of dissipation in turbulent flow, focusing on the symmetry of coefficients in equations describing energy transfer between different scales. Investigate the core principle of the Strong Onsager Conjecture, which posits that energy transfer between scales in turbulent flows should be direction-independent. Learn about the significance of this conjecture in understanding and modeling vortices, turbulence, and energy transfer in various physical systems. Gain insights into why this active area of research continues to challenge the physics community, as it awaits general mathematical confirmation. This first part of the lecture series specifically addresses the local energy inequality, providing a foundation for understanding these complex concepts in fluid dynamics and turbulence theory.