Counterexamples to Strichartz estimates for the magnetic Schrödinger equation

Abstract

In space dimension n < 3, we consider the magnetic Schrödinger Hamiltonian H = -(∇ - iA(x))2 and the corresponding Schrödinger equation iτu + 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