Counterexamples to Strichartz estimates for the magnetic Schroedinger equation

Details Counterexamples to Strichartz estimates for the magnetic Schroedinger equation Counterexamples to Strichartz estimates for the magnetic Schroedinger equation

2009-04-07

arxiv.org/abs/0904.1129v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

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.

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