The Navier-Stokes equations: on the existence of a weak solution enjoying the energy equality

Abstract

Under the assumption of an initial datum divergence free and in L2, we prove the existence of a weak solution to the Navier-Stokes initial boundary value problem enjoying the energy equality on (0,t), almost everywhere in t>0, in particular, for all t $\in [\theta, \infty)$, with $\theta := \theta(||v0||2)$. Also, the result allows us to refine some others.