The strong Onsager conjecture

The phenomenon of anomalous dissipation in turbulence predicts the existence of solutions to the incompressible Euler equations that enjoy regularity consistent with Kolmogorov’s 4/5 law and satisfy a local energy inequality. The "strong Onsager conjecture" asserts that such solutions do indeed exist. In this talk, we will discuss the background and motivation behind the strong Onsager conjecture. In addition, we outline a construction of solutions with regularity (nearly) consistent with the 4/5 law, thereby proving the conjecture in the natural L^3 scale of Besov spaces. This is based on joint work with Hyunju Kwon and Vikram Giri.