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THE GLOBAL CAUCHY PROBLEM FOR THE NLS WITH HIGHER ORDER ANISOTROPIC DISPERSION

Part of: Equations of mathematical physics and other areas of application Partial differential equations

Published online by Cambridge University Press:  12 December 2019

LEONID CHAICHENETS  and
NIKOLAOS PATTAKOS
LEONID CHAICHENETS
Affiliation:
Department of Mathematics, Institute for Analysis, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany e-mails: leonid.chaichenets@kit.edu; nikolaos.pattakos@kit.edu
NIKOLAOS PATTAKOS
Affiliation:
Department of Mathematics, Institute for Analysis, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany e-mails: leonid.chaichenets@kit.edu; nikolaos.pattakos@kit.edu
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Abstract

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We use a method developed by Strauss to obtain global well-posedness results in the mild sense and existence of asymptotic states for the small data Cauchy problem in modulation spaces ${M}^s_{p,q}(\mathbb{R}^d)$, where q = 1 and $s\geq0$ or $q\in(1,\infty]$ and $s>\frac{d}{q'}$ for a nonlinear Schrödinger equation with higher order anisotropic dispersion and algebraic nonlinearities.

MSC classification

Primary: 35A01: Existence problems 35A02: Uniqueness problems 35Q55: NLS-like equations (nonlinear Schrödinger)
Secondary: 35B40: Asymptotic behavior of solutions
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 1 , January 2021 , pp. 45 - 53
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© Glasgow Mathematical Journal Trust 2019

References

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