Shinbrot Type Criteria for Energy Conservation of the Compressible Navier-Stokes Equations

Abstract

We prove that weak solutions to the compressible Navier-Stokes equations satisfy the energy equality under a Shinbrot-type regularity criterion. Our method applies to the fluids with both constant and degenerate viscosity and relies on a novel weak-type commutator estimate. These criterion are strictly weaker than those required in prior works [Arch. Ration. Mech. Anal., 225 (2017)] and [SIAM J. Math. Anal. 52 (2020)].