Ill-posedness of equations of inviscid fluid mechanics

We will discuss how some recent developments in the ill-posedness analysis of the 2D and 3D Euler equations help understand some phenomena of turbulence of fluids. In particular, we will see how some anisotropic initial conditions give rise to unique local-in-time solutions that can be analyzed quantitatively well below the local well-posedness regime and feature dramatic loss of regularity for positive times.