A Short but Up-to-Date Introduction to Partially Parabolic or Dissipative Systems - Lecture 1

Explore a comprehensive lecture on partially parabolic or dissipative systems in fluid mechanics. Delve into the fundamental concepts of Navier-Stokes and Euler equations, examining their role in describing nonlinear physical phenomena across physics, engineering, finance, and biology. Gain insights into recent groundbreaking techniques and seminal results in fluid flow research, including the Onsager conjecture, De Lellis and Szekelyhidi Jr.'s proof, and Buckmaster and Vicol's work on weak solutions. Investigate topics such as the full resolution of the Onsager conjecture, intermittent construction for Navier-Stokes equations, H^{1/2} weak solutions of incompressible 3D Euler equations, and stochastic convex integration methods. Benefit from the expertise of leading researcher Raphaël Danchin in this 1 hour 22 minute lecture, part of the "Deterministic and Stochastic Analysis of Euler and Navier-Stokes Equations" program organized by the International Centre for Theoretical Sciences.