Local Dissipation of Energy for Continuous Incompressible Euler Flows

I will discuss the construction of continuous solutions to the incompressible Euler equations that exhibit local dissipation of energy and the surrounding motivations. A significant open question, which represents a strong form of the Onsager conjecture, is whether such solutions exist that locally dissipate energy while having the maximal possible regularity of being 1/3-Hölder continuous.