On the well-posedness of the Cauchy problem for some nonlocal nonlinear Schrödinger equations

Nonlinearity ◽  
2017 ◽  
Vol 30 (6) ◽  
pp. 2308-2333 ◽  
Author(s):  
John Albert ◽  
Estapraq Kahlil
Keyword(s):  
Cauchy Problem ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Well Posedness ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Cauchy Problem ◽  
Nonlocal Nonlinear

scholarly journals On the stochastic nonlinear Schrödinger equations at critical regularities

2020 ◽  
Vol 8 (4) ◽  
pp. 869-894
Author(s):  
Tadahiro Oh ◽  
Mamoru Okamoto
Keyword(s):  
Additive Noise ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Well Posedness ◽  
Stochastic Pde ◽  
Schrödinger Equations ◽  
Random Data ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Cauchy Problem

AbstractWe consider the Cauchy problem for the defocusing stochastic nonlinear Schrödinger equations (SNLS) with an additive noise in the mass-critical and energy-critical settings. By adapting the probabilistic perturbation argument employed in the context of the random data Cauchy theory by Bényi et al. (Trans Am Math Soc Ser B 2:1–50, 2015) to the current stochastic PDE setting, we present a concise argument to establish global well-posedness of the mass-critical and energy-critical SNLS.

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