Energy conservation for the compressible Euler system

We prove the local energy equality for the isentropic compressible Euler equations under the
assumption of the Besov regularity in space and the Bochner integrability in time. We show that this

result can be established in a certain class of exponents determining the regularity. We also use the Paley-
Littlewood decomposition to extend the energy equality to the case of the threshold exponent.