  We assert that the solutions to the Cauchy problem of the inviscid vorticity
equation remain regular and unique for any smooth initial data of finite
energy. However, the primitive formulation of the Euler equations is not
well-posed, due to the passive pressure. One of the implications is that the
anomalous energy dissipation, anticipated by Onsager (1949), cannot occur in
inviscid flows. In the complete absence of viscous effects, the ultimate
accumulation of enstrophy in sealed domains is bound to become arbitrarily
excessive, if there is a sustained supply of shears and strains.
