Counterexamples to Strichartz estimates for the magnetic Schroedinger equation
arXiv:0904.1129
Abstract
In space dimension $n\geq3$, we consider the magnetic Schrödinger Hamiltonian $H=-(\nabla-iA(x))^2$ and the corresponding Schrödinger 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 Schrödinger admissibility.
17 pages