  We consider the 3D Euler equations for incompressible homogeneous fluids and
we study the problem of energy conservation for weak solutions in the
space-periodic case. First, we prove the energy conservation for a full scale
of Besov spaces, by extending some classical results to a wider range of
exponents. Next, we consider the energy conservation in the case of conditions
on the gradient, recovering some results which were known, up to now, only for
the Navier-Stokes equations and for weak solutions of the Leray-Hopf type.
Finally, we make some remarks on the Onsager singularity problem, identifying
conditions which allow to pass to the limit from solutions of the Navier-Stokes
equations to solution of the Euler ones, producing weak solutions which are
energy conserving.
