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

We study in this article the mathematical properties of a class of orbital-free kinetic energy functionals. We prove that these models are linearly stable but nonlinearly unstable, in the sense that the corresponding kinetic energy functionals are not bounded from below. As a matter of illustration, we provide an example of an electronic density of simple shape the kinetic energy of which is negative.