On the energy equality for distributional solutions to Navier–Stokes equations

Galdi, Giovanni

doi:10.1090/proc/14256

On the energy equality for distributional solutions to Navier–Stokes equations
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Proc. Amer. Math. Soc. 147 (2019), 785-792 Request permission

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.

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