Regularity and Energy Conservation for the Compressible Euler Equations
  We give sufficient conditions on the regularity of solutions to the inhomogeneous incompressible Euler and the compressible isentropic Euler systems in order for the energy to be conserved. Our strategy relies on commutator estimates similar to those employed by P. Constantin et al. for the homogeneous incompressible Euler equations. 
Eduard Feireisl, Piotr Gwiazda, Agnieszka \'Swierczewska-Gwiazda, Emil   Wiedemann
math.AP