Explore a comprehensive analysis seminar on the construction of continuous solutions to incompressible Euler equations exhibiting local energy dissipation. Delve into the motivations behind this research, including weak solutions, energy conservation in smooth solutions, and hydrodynamic turbulence. Examine Onsager's Conjecture and its implications for ideal turbulence, as well as the K41 Folklore Conjecture for Navier-Stokes equations. Investigate the open problem of the Strong Onsager conjecture and recent theorems addressing it. Learn about the Euler-Reynolds equations, convex integration techniques, and the challenges in eliminating unresolved flux currents and stress. Gain insights into the speaker's approach to constructing solutions with local energy dissipation while maintaining the highest possible regularity.