  Onsager conjectured that solutions of the incompressible Euler equations
possessing a certain degree of roughness do not conserve the kinetic energy.
Since, within the physical frame of Onsager's conjecture, the kinetic energy is
the only occurring energy, and thus identical with the total energy, the
implication would be that the conservation of energy is not absolute, but
subject to the properties of mathematical solutions. Further, Onsager
introduced the concept of anomalous dissipation of kinetic energy without
viscosity. Both these aspects are critically discussed and their shortcomings
unveiled.
