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Gravitational Riemann Invariants
Authors: Ph. Choquard
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One-dimensional, inviscid, compressible and isentropic fluids under gravity are considered,
here, as usefull preambles relevant to the theory of uni-axial meteorological phenomena,[4] .We shaw
that there are two new Riemann invariants, [1], incorporating gravity, which are constants of the
motion. Expressing the mass densities occuring in these Invariants as product of their initial values
times the inverse Jacobian of the characteristics of these fluids with respect to their initial values,
we propose, central in this work, first order non-linear PDE’s of Charpit type [2] satisfied by these
invariants. Examples of solutions are given and checked to conform with results of, gravity-free,
similar PDE’s published in [3].