  In this paper we study the problem of energy conservation for the solutions
of the initial boundary value problem associated to the 3D Navier-Stokes
equations, with Dirichlet boundary conditions. First, we consider Leray-Hopf
weak solutions and we prove some new criteria, involving the gradient of the
velocity. Next, we compare them with the existing literature in scaling
invariant spaces and with the Onsager conjecture. Then, we consider the problem
of energy conservation for very-weak solutions, proving energy equality for
distributional solutions belonging to the so-called Shinbrot class. A possible
explanation of the role of this classical class of solutions, which is not
scaling invariant, is also given.
