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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Detalles Bibliográficos
Autores: Fanelli, Luca, García Alonso, Andoni
Tipo de recurso: artículo
Fecha de publicación:2011
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/69691
Acceso en línea:http://hdl.handle.net/10810/69691
Access Level:acceso abierto
Palabra clave:Strichartz estimates
dispersive equations
Schrödinger equation
magnetic potential
Descripción
Sumario: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