Explore the fourth lecture in a series on partially parabolic equations, delivered by Raphaël Danchin at the International Centre for Theoretical Sciences. Delve into advanced topics in fluid mechanics as part of the program on Deterministic and Stochastic Analysis of Euler and Navier-Stokes Equations. Gain insights into recent developments in nonlinear partial differential equations, including the Onsager conjecture, weak solutions to Euler and Navier-Stokes equations, and stochastic fluid flow equations. Benefit from expert discussions on cutting-edge techniques in the field of fluid mechanics during this 1 hour and 45 minute presentation.