Well-posedness of the Two-dimensional Nonlinear Schr\"odinger Equation with Concentrated Nonlinearity
Mathematical Physics
2019-02-06 v2 Analysis of PDEs
math.MP
Quantum Physics
Abstract
We consider a two-dimensional nonlinear Schr\"odinger equation with concentrated nonlinearity. In both the focusing and defocusing case we prove local well-posedness, i.e., existence and uniqueness of the solution for short times, as well as energy and mass conservation. In addition, we prove that this implies global existence in the defocusing case, irrespective of the power of the nonlinearity, while in the focusing case blowing-up solutions may arise.
Keywords
Cite
@article{arxiv.1702.03651,
title = {Well-posedness of the Two-dimensional Nonlinear Schr\"odinger Equation with Concentrated Nonlinearity},
author = {Raffaele Carlone and Michele Correggi and Lorenzo Tentarelli},
journal= {arXiv preprint arXiv:1702.03651},
year = {2019}
}
Comments
39 pages, pdfLaTex. Final version to appear in Ann. I. H. Poincar\'e - AN