Smooth (spatially periodic) solutions to the incompressible 3D Euler equations have kinetic energy conservation in every local region, while turbulent flows exhibit anomalous dissipation of energy. Toward verification of the anomalous dissipation, Onsager theorem has been established, which says that the threshold Hölder regularity of the total kinetic energy conservation is 1/3. As a next step, we discuss a strong Onsager conjecture, which combines the Onsager theorem with the local energy inequality.