Euler flows with local energy dissipation

The incompressible 3D Euler equations have total kinetic energy conservation for smooth (spatially periodic) solutions. In the recent resolution of the Onsager conjecture by Isett, on the other hand, below certain threshold Hölder regularity, Euler flows with total kinetic energy dissipation have been constructed. In this talk, I'll discuss the construction of Euler flows with kinetic energy dissipation in every local region. I'll also talk about an analogous question for the isentropic compressible Euler equations. The talk will be based on joint works with Camillo De Lellis and Vikram Giri.