scholarly journals The local well-posedness for nonlinear fourth-order Schrödinger equation with mass-critical nonlinearity and derivative

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Cuihua Guo ◽  
Shulin Sun ◽  
Hongping Ren
Keyword(s):  
Schrödinger Equation ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Well Posedness ◽  
Critical Nonlinearity

scholarly journals GLOBAL WELL-POSEDNESS FOR THE GENERALISED FOURTH-ORDER SCHRÖDINGER EQUATION

2012 ◽  
Vol 85 (3) ◽  
pp. 371-379 ◽  
Author(s):  
YUZHAO WANG
Keyword(s):  
Cauchy Problem ◽  
Schrödinger Equation ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Vries Equation ◽  
Well Posedness ◽  
Small Initial Data ◽  
The Cauchy Problem ◽  
Image Position ◽  
Appl Math

AbstractWe study the Cauchy problem for the generalised fourth-order Schrödinger equation for data u0 in critical Sobolev spaces $\dot {H}^{1/2-3/2k}$. With small initial data we obtain global well-posedness results. Our proof relies heavily on the method developed by Kenig et al. [‘Well-posedness and scattering results for the generalised Korteweg–de Vries equation via the contraction principle’, Commun. Pure Appl. Math.46 (1993), 527–620].

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