A Short but Up-to-Date Introduction to Partially Parabolic Systems - Lecture 4

Explore a comprehensive lecture on partially parabolic equations in this fourth installment of a series by Raphaël Danchin. Delve into advanced mathematical concepts related to fluid dynamics, focusing on the Navier-Stokes and Euler equations. Gain insights into recent developments in the field, including the Onsager conjecture, weak solutions, and stochastic fluid flow equations. Examine groundbreaking techniques and seminal results that have shaped the understanding of nonlinear partial differential equations in physics, engineering, finance, and biology. Engage with complex topics such as statistical hydrodynamics, energy conservation in weak solutions, and the application of convex integration methods to stochastic systems.