Explore recent advancements in the well-posedness theory of incompressible Navier-Stokes and Euler equations in this 53-minute lecture by Maria Colombo from EPFL. Delve into the surprising progress made over the past decade in describing non-unique solutions to these fundamental partial differential equations in mathematical fluid dynamics. Examine various approaches to this complex problem, including works in collaboration with Albritton and Brué that demonstrate the non-uniqueness of Leray-Hopf solutions for forced Navier-Stokes equations. Gain insights into the current state of research and open questions in this critical area of fluid dynamics.