Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 1, pp. 257-294.
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We consider a two-dimensional nonlinear Schrödinger 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.

DOI : 10.1016/j.anihpc.2018.05.003
Mots-clés : Nonlinear Schrödinger equation, Point interactions, Volterra equations 
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     title = {Well-posedness of the two-dimensional nonlinear {Schr\"odinger} equation with concentrated nonlinearity},
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Carlone, Raffaele; Correggi, Michele; Tentarelli, Lorenzo. Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 1, pp. 257-294. doi : 10.1016/j.anihpc.2018.05.003. http://www.numdam.org/articles/10.1016/j.anihpc.2018.05.003/

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