Global L∞ entropy solutions of the isentropic nozzle Euler equations constructed by the author's Godunov scheme are shown to satisfy the mechanical energy inequality whenever the initial weighted energy is finite.
LeFloch, Michael Westdickenberg: Finite energy solutions to the isentropic Euler equations with geometric effects
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Remarks on the energy inequality of a global $L^{\infty}$ solution to the compressible Euler equations for the isentropic nozzle flow
Global L∞ entropy solutions of the isentropic nozzle Euler equations constructed by the author's Godunov scheme are shown to satisfy the mechanical energy inequality whenever the initial weighted energy is finite.