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On the global well-posedness of the quadratic NLS on $L^2(\mathbb{R})+H^1(\mathbb{R})$

Chaichenets, Leonid; Hundertmark, Dirk; Kunstmann, Peer; Pattakos, Nikolaos

Abstract:
We study the one dimensional nonlinear Schrödinger equation with power nonlinearity $|u|^{\alpha-1}$ for $\alpha \in [2, 5]$ and initial data $u_0 ∈ L^2(\mathbb{R})+H^1(\mathbb{T})$. We show via Strichartz estimates that the Cauchy problem is locally well-posed. In the case of the quadratic nonlinearity $(\alpha = 2)$ we obtain unconditional global well-posedness in the space $C(\mathbb{R}, L^2(\mathbb{R})+H^1(\mathbb{T}))$ via Gronwall’s inequality.

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Volltext §
DOI: 10.5445/IR/1000093752
Veröffentlicht am 16.04.2019
Coverbild
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2019
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000093752
Verlag KIT, Karlsruhe
Umfang 23 S.
Serie CRC 1173 ; 2019/9
Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagworte nonlinear Schrödinger equation, local well-posedness, global well-posedness, Gronwall’s inequality, Strichartz estimates
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