Counterexamples to Strichartz estimates for the magnetic Schrödinger equation

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 estim...

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Bibliographic Details
Authors: Fanelli, Luca, García Alonso, Andoni
Format: article
Publication Date:2011
Country:España
Institution:Universidad del País Vasco
Repository:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/69691
Online Access:http://hdl.handle.net/10810/69691
Access Level:Open access
Keyword:Strichartz estimates
dispersive equations
Schrödinger equation
magnetic potential
Description
Summary: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