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arXiv · 0904.1129

Counterexamples to Strichartz estimates for the magnetic Schroedinger equation

Luca Fanelli·Andoni Garcia
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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.

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Luca Fanelli, Andoni Garcia. 2009-04-07. Counterexamples to Strichartz estimates for the magnetic Schroedinger equation. https://arxiv.org/abs/0904.1129

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