scholarly journals Global well-posedness below the ground state for the nonlinear Schrödinger equation with a linear potential

2020 ◽  
Vol 148 (12) ◽  
pp. 5193-5207
Author(s):  
Masaru Hamano ◽  
Masahiro Ikeda
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Linear Potential ◽  
Well Posedness ◽  
Nonlinear Schrödinger

ON ONE BLOW UP POINT SOLUTIONS TO THE CRITICAL NONLINEAR SCHRÖDINGER EQUATION

2005 ◽  
Vol 02 (04) ◽  
pp. 919-962 ◽  
Author(s):  
FRANK MERLE ◽  
PIERRE RAPHAEL
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Ground State ◽  
Finite Time ◽  
Schrodinger Equation ◽  
Blow Up ◽  
Nonlinear Schrodinger Equation ◽  
Specific Class ◽  
Nonlinear Schrödinger ◽  
Existence And Stability

We consider the L2 critical nonlinear Schrödinger equation [Formula: see text] in the energy space H1. In the series of papers [11–15,18], we studied finite time blow up solutions for which lim t↑T < + ∞ |∇ u(t)|L2 = + ∞ and proved classification results of the blow up dynamics for the specific class of small super critical L2 mass initial data. We extend these results here to a wider class of finite time blow up solutions corresponding to the ones which accumulate at one point exactly the ground state mass. In particular, we prove the existence and stability of large L2 mass log-log type solutions which are believed to describe the generic blow up dynamics.

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.

Sign in / Sign up

Export Citation Format

Share Document