Energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations

We study the local energy equation for weak solutions of 3D incompressible Euler and Navier-Stokes equations. We introduce a dissipation term coming f rom an eventual lack of regularity in the solution. We use this local energ y equation to give a simple proof of Onsager's conjecture, slightly improvi ng the hypothesis given in [1]. We propose a new notion, of dissipative sol ution for such weak solutions. (C) Academie des Sciences/Elsevier, Paris.