On the Energy Equality for Distributional Solutions to Navier-Stokes Equations

Abstract

A classical result of J.-L. Lions asserts that if a solution to the Navier-Stokes equations is such that: (i) it is in the Leray-Hopf class, and (ii) belongs to $L^4(0,T;L^4)$, then it must satisfy the energy equality in the time interval $[0,T]$. In this note we show that assumption (i) is not necessary.