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Low regularity well-posedness for generalized Benjamin–Ono equations on the circle

Kim, Kihyun; Schippa, Robert

Abstract:
New low regularity well-posedness results for the generalized Benjamin-Ono equations with quartic or higher nonlinearity and periodic boundary conditions are shown. We use the short-time Fourier transform restriction method and modified energies to overcome the derivative loss. Previously, Molinet–Ribaud established local well-posedness in $H^1(\mathbb{T},\mathbb{R})$ via gauge transforms. We show local existence and a priori estimates in $H^s(\mathbb{T},\mathbb{R}),$ $s>1/2$, and local well-posedness in $H^s(\mathbb{T},\mathbb{R})$, $s\ge3/4$ without using gauge transforms. In case of quartic nonlinearity we prove global existence of solutions conditional upon small initial data.

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Volltext §
DOI: 10.5445/IR/1000122682
Veröffentlicht am 14.08.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 08.2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000122682
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 45 S.
Serie CRC 1173 Preprint ; 2020/23
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter dispersive equations, quasilinear equations, generalized Benjamin-Ono equation, short-time Fourier restriction
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