Existence of a weak solution to the Navier-Stokes equations enjoying the energy equality

To date, a Leray's weak solution to the Navier-Stokes equations enjoys an energy inequality. We prove the existence of a weak solution that enjoys the energy equality. The existence of the weak solution is achieved as limit of solutions to the mollified Navier-Stokes system (Leray's approach). Since no uniqueness result is known for weak solutions we are not able to claim that any weak solution in the sense of Leray-Hopf enjoys the energy equality.