On the Flow Map and the Partial Differential Equations Associated to a Non-Smooth Vector Field

Explore a comprehensive lecture on the flow map and partial differential equations associated with non-smooth vector fields in fluid dynamics. Delve into advanced mathematical concepts related to the Euler and Navier-Stokes equations, focusing on recent developments in the field of fluid mechanics. Examine the Onsager conjecture, energy conservation in weak solutions, and groundbreaking techniques in statistical hydrodynamics. Gain insights into 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. Suitable for PhD students, postdocs, and faculty members working on mathematical aspects of fluid flow equations.