Inertial energy dissipation for weak solutions of incompressible Euler andNavier-Stokes equations

We study the local equation of energy for weak solutions of three-dimension al incompressible Navier-Stokes and Euler equations. We define a dissipatio n term D(u) which stems from an eventual lack of smoothness in the solution u. We give in passing a simple proof of Onsager's conjecture on energy con servation for the three-dimensional Euler equation, slightly weakening the assumption of Constantin et al. We suggest calling weak solutions with non- negative D(u) 'dissipative'.