Counterexamples to Strichartz estimates for the magnetic Schroedinger equation

Luca Fanelli; Andoni Garcia

Counterexamples to Strichartz estimates for the magnetic Schroedinger equation

Analysis of PDEs 2009-04-08 v1

Authors: Luca Fanelli , Andoni Garcia

Abstract

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.

Keywords

schrödinger equation

Cite

@article{arxiv.0904.1129,
  title  = {Counterexamples to Strichartz estimates for the magnetic Schroedinger equation},
  author = {Luca Fanelli and Andoni Garcia},
  journal= {arXiv preprint arXiv:0904.1129},
  year   = {2009}
}

Comments

17 pages

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