Dependence of the nonlinear Schrödinger flow upon the nonlinearity
Rémi Carles1  ; Quentin Chauleur2  ; Guillaume Ferriere2
1CNRS, IRMAR - UMR 6625, F-35000 Rennes, France
2Univ. Lille, CNRS, Inria, UMR 8524 - Laboratoire Paul Painlevé, F-59000 Lille, France
Séminaire Laurent Schwartz — EDP et applications (2025), Exposé no. 13, 13 p.

We consider the defocusing nonlinear Schrödinger equation in the energy-subcritical case, and investigate the dependence of the solution upon the power of the nonlinearity. Special attention is paid to the global in time description. The main three aspects addressed, in the decreasing order of difficulty, are the limit when the total power tends to one, along with the connection with the logarithmic Schrödinger equation, the description when long range effects may be present, and the continuity of the scattering operator in the short range case. This text resumes the presentation given by the first author at École polytechnique for the Laurent Schwartz seminar, in May 2026.

Publié le :
DOI : 10.5802/slsedp.183

Rémi Carles  1   ; Quentin Chauleur  2   ; Guillaume Ferriere  2

1 CNRS, IRMAR - UMR 6625, F-35000 Rennes, France
2 Univ. Lille, CNRS, Inria, UMR 8524 - Laboratoire Paul Painlevé, F-59000 Lille, France 
Rémi Carles; Quentin Chauleur; Guillaume Ferriere. Dependence of the nonlinear Schrödinger flow upon the nonlinearity. Séminaire Laurent Schwartz — EDP et applications (2025), Exposé no. 13, 13 p.. doi: 10.5802/slsedp.183
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     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
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