Calculus of Variations and Geometric Measure Theory

R. Carlone - M. Correggi - L. Tentarelli

Well-posedness of the Two-dimensional Nonlinear Schrödinger Equation with Concentrated Nonlinearity

created by tentarelli on 07 Jul 2022


Published Paper

Inserted: 7 jul 2022
Last Updated: 7 jul 2022

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Volume: 36
Number: 1
Pages: 257-294
Year: 2019
Doi: 10.1016/j.anihpc.2018.05.003

ArXiv: 1702.03651 PDF


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.