Emil Wiedemann - On the Conservation of Energy-Entropy in Fluid Dynamics

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.

Intro
Incompressible Euler Equations Consider the incompressible Euer equations
Onsager's Conjecture/Theorem
The Commutator Estimate
Energy Conservation
Dissipative vs. Conservative Solutions
An Onsager-Type Result for Compressible Euler
Remarks
The Pressure Commutator
General Conservation Laws
Example: Incompressible Euler
Entropy Conservation
Idea of proof
Improvement on the Besov Condition
Some Examples