  We prove that the initial value problem for Force-free Electrodynamics in
Euler variables is not well posed. We establish this result by showing that a
well-posedness criterion provided by Kreiss fails to hold for this theory, and
using a theorem provided by Strang. To show the nature of the problem we
display a particular bounded (in Sobolev norms) sequence of initial data for
the Force-free equations such that at any given time as close to zero as one
wishes, the corresponding evolution sequence is not bounded. Thus, the
Force-free evolution is non continuous in that norm with respect to the initial
data. We furthermore prove that this problem is also ill-posed in the
Leray-Ohya sense.
