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...
| Authors: | , |
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| 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 |
| 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 |
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