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

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 nonli...

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Published inGlasgow mathematical journal Vol. 63; no. 1; pp. 45 - 53
Main Authors CHAICHENETS, LEONID, PATTAKOS, NIKOLAOS
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.01.2021
Subjects
Cauchy problems
Dispersion
Schrodinger equation
35Q55
35B40
35A02
35A01
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Summary: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.
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SourceType-Scholarly Journals-1
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ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089519000491