Explore the intricacies of energy and entropy conservation in fluid dynamics through this 55-minute lecture by Emil Wiedemann. Delve into Onsager's Conjecture and its implications for incompressible Euler equations, examining the threshold of regularity for energy conservation. Investigate recent developments in generalizing and improving the theory, addressing topics such as general conservation laws, boundary effects, critical function spaces, and degenerate situations like vacuum formation in compressible fluids. Learn about the commutator estimate, dissipative vs. conservative solutions, and an Onsager-type result for compressible Euler equations. Analyze the pressure commutator, entropy conservation, and improvements on the Besov condition, with practical examples provided throughout the lecture.