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On the global wellposedness of the Klein-Gordon equation for initial data in modulation spaces

Chaichenets, Leonid; Pattakos, Nikolaos

Abstract:
We prove global wellposedness of the Klein-Gordon equation with power nonlinearity $|u|^{\alpha−1}u$, where $\alpha\in\left[1,\frac{d}{d−2}\right]$, in dimension $d\ge3$ with initial data in $M^1_{p,p'}(\mathbb{R}^d)\times M_{p,p'}(\mathbb{R}^d)$ for $p$ sufficiently close to $2$. The proof is an application of the high-low method
described by Bourgain in [1] where the Klein-Gordon equation is studied in one dimension with cubic nonlinearity for initial data in Sobolev spaces.

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Volltext §
DOI: 10.5445/IR/1000099117
Veröffentlicht am 18.10.2019
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: 1000099117
Verlag KIT, Karlsruhe
Umfang 12 S.
Serie CRC 1173 ; 2019/18
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Schlagworte Klein-Gordon equation, modulation spaces, global wellposedness, high-low frequency decomposition method
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