  In space dimension $n\geq3$, we consider the magnetic Schr\"odinger
Hamiltonian $H=-(\nabla-iA(x))^2$ and the corresponding Schr\"odinger equation
i\partial_tu+Hu=0. We show some explicit examples of potentials $A$, with less
than Coulomb decay, for which any solution of this equation cannot satisfy
Strichartz estimates, in the whole range of Schr\"odinger admissibility.
