  Onsager's conjecture for the 3D Navier-Stokes equations concerns the validity
of energy equality of weak solutions with regards to their smoothness. In this
note we establish energy equality for weak solutions in a large class of
function spaces. These conditions are weak-in-time with optimal space
regularity and therefore weaker than all previous classical results. Heuristics
using intermittency argument suggests the possible sharpness of our results.
