Counterexamples to Strichartz estimates for the magnetic Schroedinger equation

Abstract

In space dimension $n\ge 3$, 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

References in corpus (1)

• Endpoint Strichartz estimates for the magnetic Schrodinger equation