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We study in this article the mathematical properties of a class oforbital-free kinetic energy functionals. We prove that these models arelinearly stable but nonlinearly unstable, in the sense that the correspondingkinetic energy functionals are not bounded from below. As a matter ofillustration, we provide an example of an electronic density of simple shapethe kinetic energy of which is negative.Comment: 14 pages, 1 figur

Nonlinear instability of density-independent orbital-free kinetic-energy functionals