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July/August 2013 Resonant phase-shift and global smoothing of the periodic Korteweg-de Vries equation in low regularity settings
Seungly Oh
Adv. Differential Equations 18(7/8): 633-662 (July/August 2013).

Abstract

We show a smoothing effect of near full-derivative for low-regularity global-in-time solutions of the periodic Korteweg--de Vries (KdV) equation. The smoothing is given by slightly shifting the space-time Fourier support of the nonlinear solution, which we call resonant phase-shift. More precisely, we show that $\mathcal{S}[u](t) - e^{-t{\partial}_x^3} u(0) \in H^{-s+1-}$, where $u(0) \in H^{-s}$ for $0\leq s < 1/2$ where $\mathcal{S}$ is the resonant phase-shift operator described below. We use the normal form method to obtain the result.

Citation

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Seungly Oh . "Resonant phase-shift and global smoothing of the periodic Korteweg-de Vries equation in low regularity settings." Adv. Differential Equations 18 (7/8) 633 - 662, July/August 2013.

Information

Published: July/August 2013
First available in Project Euclid: 20 May 2013

zbMATH: 1291.35303
MathSciNet: MR3086670

Subjects:
Primary: 35B10 , 35B30 , 5Q53

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.18 • No. 7/8 • July/August 2013
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