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An hydrodynamic description of a one-dimensional flow of an ideal Fermi fluidis constructed from a semiclassical approximation. For an initially fullydegenerate fluid, Euler and continuity hydrodynamic equations are dual to twouncoupled inviscid Burgers' equations. Yet the price for the initial simplicityof the description is paid by the complexity of non-linear instabilitiestowards possible turbulent evolutions. Nevertheless, it is shown that linearlong-wavelength density perturbations on a stationary flow are genericallystable. Consequently, linear sound obeys a wave equation with analogy togravity. The results have applications for ultra-cold atomic gases.

Gravity-analogy in one-dimensional ideal Fermi fluids and Burgers' equation