scholarly journals Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrödinger equation

2006 ◽  
Vol 233 (1) ◽  
pp. 228-259 ◽  
Author(s):  
Ioan Bejenaru ◽  
Terence Tao
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Well Posedness ◽  
Non Linear

scholarly journals ON GLOBAL ROUGH SOLUTIONS TO A NON-LINEAR SCHRÖDINGER SYSTEM

2009 ◽  
Vol 51 (3) ◽  
pp. 499-511 ◽  
Author(s):  
LI MA ◽  
XIANFA SONG ◽  
LIN ZHAO
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Well Posedness ◽  
Nonlinear Schrödinger ◽  
Non Linear ◽  
Schrödinger Systems ◽  
Schrödinger System

AbstractThe non-linear Schrödinger systems arise from many important physical branches. In this paper, employing the ‘I-method’, we prove the global-in-time well-posedness for a coupled non-linear Schrödinger system in Hs(n) when n = 2, s > 4/7 and n = 3, s > 5/6, respectively, which extends the results of J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao (Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation, Math Res. Lett. 9, 2002, 659–682) to the system.

Global well-posedness for the derivative non-linear Schrödinger equation

2018 ◽  
Vol 43 (8) ◽  
pp. 1151-1195 ◽  
Author(s):  
Robert Jenkins ◽  
Jiaqi Liu ◽  
Peter A. Perry ◽  
Catherine Sulem
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Well Posedness ◽  
Non Linear

Global well-posedness for discrete non-linear Schrödinger equation

2010 ◽  
Vol 89 (9) ◽  
pp. 1513-1521 ◽  
Author(s):  
Gaston M. N'Guérékata ◽  
Alexander Pankov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Well Posedness ◽  
Non Linear

scholarly journals ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS

2009 ◽  
Vol 06 (03) ◽  
pp. 549-575 ◽  
Author(s):  
J. COLLIANDER ◽  
S. IBRAHIM ◽  
M. MAJDOUB ◽  
N. MASMOUDI
Keyword(s):  
Schrödinger Equation ◽  
Initial Value Problem ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Energy Space ◽  
Well Posedness ◽  
Initial Value ◽  
Exponential Nonlinearity ◽  
Supercritical Case ◽  
Two Space Dimensions

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity [Formula: see text] We identify subcritical, critical, and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.

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