Lenzmann, Enno. (2007) Well-posedness for semi-relativistic Hartree equations of critical type. Mathematical Physics, Analysis and Geometry, 10 (1). pp. 43-64.
Full text not available from this repository.
Official URL: http://edoc.unibas.ch/49585/
Downloads: Statistics Overview
Abstract
We prove local and global well-posedness for semi-relativistic, nonlinear Schrödinger equations i∂tu=−Δ+m2 √u+F(u) with initial data in Hs(ℝ3), s⩾1/2. Here F(u) is a critical Hartree nonlinearity that corresponds to Coulomb or Yukawa type self-interactions. For focusing F(u), which arise in the quantum theory of boson stars, we derive global-in-time existence for small initial data, where the smallness condition is expressed in terms of the L2-norm of solitary wave ground states. Our proof of well-posedness does not rely on Strichartz type estimates. As a major benefit from this, our method enables us to consider external potentials of a quite general class.
Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Lenzmann) |
---|---|
UniBasel Contributors: | Lenzmann, Enno |
Item Type: | Article, refereed |
Article Subtype: | Research Article |
Publisher: | Springer |
ISSN: | 1385-0172 |
e-ISSN: | 1572-9656 |
Note: | Publication type according to Uni Basel Research Database: Journal article |
Identification Number: | |
Last Modified: | 28 Nov 2017 08:35 |
Deposited On: | 28 Nov 2017 08:35 |
Repository Staff Only: item control page