Global well-posedness and scattering for the fourth order nonlinear Schrödinger equations with small data in modulation and Sobolev spaces
File(s)
Accepted version
Author(s)
Ruzhansky, M
Wang, B
Zhang, H
Type
Journal Article
Abstract
The local well-posedness with small data in Hs(Rn)(s⩾3+max(n/2,1+)) for the Cauchy problem of the fourth order nonlinear Schrödinger equations with the third order derivative nonlinear terms were obtained by Huo and Jia [17]. In this paper we show its global well-posedness with small data in the modulation space View the MathML source and in Sobolev spaces Hn/2+7+/2. For a special nonlinear term containing only one third order derivative, we can show its global well posedness in View the MathML source and H(n+1+)/2.
Date Issued
2015-09-08
Date Acceptance
2015-09-08
Citation
Journal de Mathematiques Pures et Appliquees, 2015, 105 (1), pp.31-65
ISSN
0021-7824
Publisher
Elsevier
Start Page
31
End Page
65
Journal / Book Title
Journal de Mathematiques Pures et Appliquees
Volume
105
Issue
1
Copyright Statement
© 2015 Elsevier Masson SAS. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Global well-posedness
Fourth order nonlinear Schrodinger equations
Small initial data
Modulation and Sobolev spaces
UNIMODULAR FOURIER MULTIPLIERS
HIGHER-ORDER DISPERSION
CAUCHY-PROBLEM
REGULARITY
REPRESENTATION
OPERATORS
MAPS
NLS
General Mathematics
0101 Pure Mathematics
0102 Applied Mathematics
Publication Status
Published