Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only! Grab it Explore the mathematical theory of incompressible fluids in this 1-hour 14-minute lecture by Mimi Dai from the University of Illinois, Chicago. Delve into the pioneering work of Leray on weak solutions for the Navier-Stokes equation (NSE) and examine Ladyzhenskaya's fundamental contributions to unique solvability and global attractor problems. Discover recent findings on the regularity and long-term behavior of NSE solutions, and investigate their connections to Kolmogorov's turbulence theory. Gain insights into the ongoing challenges in fluid dynamics and the progress made since the groundbreaking work of Leray and Ladyzhenskaya.