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Classification of conservation laws of compressible isentropic fluid flow in n>1 spatial dimensions

2009
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Proceedings of the Royal Society A
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For the Euler equations governing compressible isentropic fluid flow with a barotropic equation of state (where pressure is a function only of the density), local conservation laws in $n>1$ spatial dimensions are fully classified in two primary cases of physical and analytical interest: (1) kinematic conserved densities that depend only on the fluid density and velocity, in addition to the time and space coordinates; (2) vorticity conserved densities that have an essential dependence on the

doi:10.1098/rspa.2009.0072
fatcat:x3h3fxhigbhb5fly5sv2pjikyi